rational curves and rational singularities we study rational curves on algebraic varieties especially on normal affine varieties endowed with a action for varieties with an isolated singularity covered by a family of rational curves with a general member not passing through the singular point we show that this singularity is rational in particular this provides an explanation of classical results due to h a schwartz and g h halphen on polynomial solutions of the generalized fermat equation

new abstract hardy spaces the aim of this paper is to propose an abstract construction of spaces which keep the main properties of the already known hardy spaces h1 we construct spaces through an atomic or molecular decomposition we prove some results about continuity from these spaces into l1 and some results about interpolation between these spaces and the lebesgue spaces we also obtain some results on weighted norm inequalities finally we present partial results in order to understand a characterization of the duals of hardy spaces

duality of hardy and bmo spaces associated with operators with heat kernel bounds the introduction and development of hardy and bmo spaces on euclidean spaces r in the 1960s and 1970s played an important role in modern harmonic analysis and applications in partial differential equations these spaces were studied extensively in 32 22 18 19 31 and many others an l function f on r is in the hardy spaceh r if the area integral function of the poisson integral e t f satisfies

abstract hardy sobolev spaces and interpolation the purpose of this work is to describe an abstract theory of hardy sobolev spaces on doubling riemannian manifolds via an atomic decomposition we study the real interpolation of these spaces with sobolev spaces and finally give applications to riesz inequalities

a t 1 theorem for non integral operators let x be a space of homogeneous type and let l be a sectorial operator with bounded holomorphic functional calculus on l 2 x we assume that the semigroup e tl t 0 satisfies davies gaffney estimates associated with l are certain approximations of the identity we call an operator t a non integral operator if compositions involving t and these approximations satisfy certain weighted norm estimates the davies gaffney and the weighted norm estimates are together a substitute for the usual kernel estimates on t in calderon zygmund theory in this paper we show under the additional assumption that a vertical littlewood paley stein square function associated with l is bounded on l 2 x that a non integral operator t is bounded on l 2 x if and only if t 1 in bmo l x and t 1 in bmo l x here bmo l x and bmo l x denote the recently defined bmo x spaces associated with l that generalize the space bmo x of john and nirenberg generalizing a recent result due to f bernicot we show a second version of a t 1 theorem under weaker off diagonal estimates which gives a positive answer to a question raised by him as an application we prove l 2 x boundedness of a paraproduct operator associated with l we moreover study criterions for a t b theorem to be valid

on maximal regularity of type lp lq under minimal assumptions for elliptic non divergence operators we prove maximal regularity of type l p l q for operators in non divergence form with complex valued measurable coefficients on r n for a certain range of q which depends on dimension and the order of the operators this is done under the sole assumption that they generate an analytic semigroup in l q thus we give for this class of operators and this range of q a positive answer to brezis question whether generation of an analytic semigroup entails maximal l p regularity for other values of q we give several additional assumptions the proof relies on a result on maximal regularity under the assumption of suitable off diagonal bounds due to s blunck and the author which we improve here these off diagonal bounds are obtained by a modification of davies technique suited to cope with operators in non divergence form and they also imply new results on the scale of l q spaces in which a given operator generates an analytic semigroup we thus obtain a completely new approach to maximal l p regularity for operators of this kind in particular for those whose highest order coefficients belong to vmo moreover we obtain extensions of recent results due to kim and krylov for operators with measurable coefficients depending on one coordinate

use of abstract hardy spaces real interpolation and applications to bilinear operators this paper can be considered as the sequel of bernicot and zhao j func anal 255 1761 1796 2008 where the authors have proposed an abstract construction of hardy spaces h1 they shew an interpolation result for these hardy spaces with the lebesgue spaces here we describe a more precise result using the real interpolation theory and we clarify the use of hardy spaces then with the help of the bilinear interpolation theory we then give applications to study bilinear operators on lebesgue spaces these ideas permit us to study singular operators with singularities similar to those of bilinear calderon zygmund operators in a far more abstract framework as in the euclidean case

vertical versus conical square functions we study the difference between vertical and conical square functions in the abstract and also in the specific case where the square functions come from an elliptic operator trans amer math soc 364 2012 no 10 5469 5489

saddlepoint expansions for directional test probabilities an expansion is derived for the conditional tail probability of a multivariate random variable given its direction from the expected value in particular if the score function of a statistical model is chosen as this variable such a conditional probability gives a test for a simple hypothesis which is asymptotically equivalent to the likelihood ratio test the expansion is of the large deviation type and is derived through the use of saddlepoint methods thus the relative error of the test probability is o n1 uniformly in a bounded set for an average of n independent replications the approximation is based on the cumulant transform for the random variable but is otherwise a simple expression in terms of chi squared distributions in the one dimensional case it reduces to the expansion obtained by lugannani and rice numerical examples show an excellent fit comparable with other saddlepoint expansions when the dimension is low even for very small sample sizes but for higher dimensions more replications are required to give a similar approximation

estimating functions and approximate conditional likelihood summary the approximate conditional likelihood method proposed by cox reid 1987 is applied to the estimation of a scalar parameter 0 in the presence of nuisance parameters the estimating function of 0 based on the approximate conditional likelihood is shown to be preferable to that based on the profile likelihood a sufficient condition for both approaches to be equivalent is given the role of parameter orthogonality is emphasized several examples including bivariate normal means with known coefficient of variation are presented

weighted norm inequalities off diagonal estimates and elliptic operators part i general operator theory and weights this is the first part of a series of four articles in this work we are interested in weighted norm estimates we put the emphasis on two results of different nature one is based on a good inequality with two parameters and the other uses calderon zygmund decomposition these results apply well to singular non integral operators and their commutators with bounded mean oscillation functions singular means that they are of order 0 non integral that they do not have an integral representation by a kernel with size estimates even rough so that they may not be bounded on all lp spaces for 1 p 8 pointwise estimates are then replaced by appropriate localized lp lq estimates we obtain weighted lp estimates for a range of p that is different from 1 8 and isolate the right class of weights in particular we prove an extrapolation theorem a la rubio de francia for such a class and thus vector valued estimates

a maximal function characterization for hardy spaces associated to nonnegative self adjoint operators satisfying gaussian estimates abstract let l be a nonnegative self adjoint operator satisfying gaussian estimates on l 2 r n in this article we give an atomic decomposition for the hardy spaces h l max p r n in terms of the nontangential maximal functions associated with the heat semigroup of l and this leads eventually to characterizations of hardy spaces associated to l via atomic decomposition or the nontangential maximal functions the proof is based on a modification of a technique due to a calderon 6

on the choice of prior distribution for the box cox transformed linear model summary the noninformative prior distribution for the parameters of the linear model transformed following box cox 1964 has the non bayesian property of depending to some extent on the data an alternative choice of prior which is not outcome dependent was suggested by pericchi 1981 but it is argued here that this prior has some undesirable features an alternative family of non outcome dependent priors is suggested leading to a noninformative prior which is closer in spirit to that proposed by box cox the posterior consequences of adopting this prior are fully explored and an example discussed

properties of sufficiency and statistical tests 1 in a previous paper dealing with the importance of properties of sufficiency in the statistical theory of small samples attention was mainly confined to the theory of estimation in the present paper the structure of small sample tests whether these are related to problems of estimation and fiducial distributions or are of the nature of tests of goodness of fit is considered further

on maximal l p regularity abstract the aim of this paper is to propose weak assumptions to prove maximal l q regularity for cauchy problem d u d t t l u t f t mainly we only require off diagonal estimates on the real semigroup e t l t 0 to obtain maximal l q regularity the main idea is to use one kind of hardy space h 1 adapted to this problem and then use interpolation results these techniques permit us to prove weighted maximal regularity too

a simple predictive density function abstract an easily computable predictive density is considered although involving a plain maximum likelihood technique it coincides with the posterior predictive density with a noninformative prior for standard situations achievements are comparable with classical inference

higher direct images of dualizing sheaves of lagrangian fibrations let f x s be a lagrangian fibration between projective varieties we prove that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i i s if s is smooth suppose that x is an irreducible symplectic manifold or a certain moduli space of semistable torsion free sheaves on a k 3 surface the hodge numbers satisfy h p q s h p q inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i where n dim s if s inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i and x is an irreducible symplectic manifold there exists a hypersurface m f of the kuranishi space of x such that every member of the kuranishi family over m f admits a lagrangian fibration over inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i

abstract hardy spaces with variable exponents abstract in this paper we introduce the definition of abstract hardy spaces with variable exponents via the atomic decomposition and molecular decomposition we prove the continuity from our variable hardy space h a t o p into l p where p r n 0 1 0 p p 1 moreover we investigate the bilinear theory finally we give an application of the abstract hardy spaces with variable exponents

the solution of the kato square root problem for second order elliptic operators on rn we prove the kato conjecture for elliptic operators on jfin more precisely we establish that the domain of the square root of a uniformly complex elliptic operator l div av with bounded measurable coefficients in ietn is the

conditional score functions some optimality results summary the conditional score function has previously been shown to generate the optimal estimating equation for a parameter of interest when the conditioning statistic is complete and sufficient for the nuisance parameters godambe 1976 the present paper generalizes these results to partial likelihood factorizations and then examines the nature of the problem when the appropriate conditioning statistics depend on the parameter of interest in this case globally optimal estimating functions are impossible a weaker criterion of optimal weighting leads to a class of estimated conditional score functions which satisfy an information equality the purpose of this paper is to develop and justify an approach based on conditional likelihood to estimation in the presence of nuisance parameters the arguments focus on the case when there is a complete and sufficient statistic s 0 for the nuisance parameters when the parameter of interest 0 is fixed an extended notion of completeness will be presented in the context of partial likelihoods the problem takes on two separate natures depending on whether the statistic s 0 truly depends on 0 or not if s s 0 is free of 0 then the conditional likelihood of the data given s has been shown to generate optimal inferential procedures giving a best estimating equation godambe 1976 and a best asymptotically normal estimator in a mixture setting lindsay 1980 if s 0 depends on 0 then it will be shown that the best estimating equation also a conditional likelihood score will generally be only locally optimal leaving no single best strategy consideration of an optimal weighting strategy yields estimators which have second order properties similar to the conditional likelihoods of the first type

operator valued fourier multiplier theorems and maximal l_p regularity we prove a mihlin type multiplier theorem for operator valued multiplier functions on umd spaces the essential assumption is r boundedness of the multiplier function as an application we give a characterization of maximal l p regularity for the generator of an analytic semigroup t t in terms of the r boundedness of the resolvent of a or the semigroup t t

the score statistic for regression transformation summary the score statistic for regression transformation using a parametric family is developedfurther a simple formula for the approximate variance matrix of score statistics basedon asymptotic theory is applied to yield the score statistic t s for regression transforma tion this is compared to atkinson s t d statistic for the same problem and yields animprovement to its standardization simulations indicate that the significance levels ofthe proposed score statistic t s are very close to their nominal values some key words power transformation regression score statistic simulation tests for normality 1 introduction the work of box cox 1964 has been the basis of many investigations into theuse of transformations in regression analysis and the current state of the topic is wellsummarized in the monographs of cook weisberg 1982 and atkinson 1985 theprincipal aim of the original work was to transform a response or dependent variable sothat it would satisfy the normality and other standard assumptions of regression analysis the authors used a parametric family of transformations to achieve this and placedemphasis on estimating its parameters in subsequent work andrews 1971 was moreconcerned with testing transformation parameters while atkinson 1973 introducedanother statistic for this purpose from consideration of both andrews s statistic and scoreor c a tests the present paper develops a standardized score statistic in the case of ascalar transformation parameter in effect it is found to provide the standardization ofatkinson s statistic an aspect which atkinson 1973 believed to be theoretically intract able and avoided by using an approximate regression argument

weighted estimates for powers and smoothing estimates of schrodinger operators with inverse square potentials abstract let l a be a schrodinger operator with inverse square potential a x 2 on r d d 3 the main aim of this paper is to prove weighted estimates for fractional powers of l a the proof is based on weighted hardy inequalities and weighted inequalities for square functions associated to l a as an application we obtain smoothing estimates regarding the propagator e i t l a

bartlett adjustments to the likelihood ratio statistic and the distribution of the maximum likelihood estimator for rather general parametric models a simple connection is established between the bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant c of the formula c i i 1 2l for the conditional distribution of a maximum likelihood estimator as applied to the full model and the model of the hypothesis tested this leads to a relatively simple demonstration that division of the likelihood ratio statistic by a suitable constant or estimated factor improves the chi squared approximation to its distribution various expressions for these quantities are discussed in particular for the case of a one dimensional parameter an approximation to the constants involved is derived which does not require integration over the sample space

a bayesian approach to transformations to normality summary the analysis of transformation of observations in the linear model with normal errors proposed by box cox 1964 is considered a different choice of noninformative unnormed prior is advocated which is not outcome dependent this new selection of prior leads to a formal identity between likelihood and bayesian inference both for the estimation of the best transformation to normality and for the presence of homoscedasticity and additivity under this transformation extension to a related problem is mentioned

hardy and bmo spaces associated to divergence form elliptic operators consider a second order divergence form elliptic operator l with complex bounded measurable coefficients in general operators based on l such as the riesz transform or square function may lie beyond the scope of the calderon zygmund theory they need not be bounded in the classical hardy bmo and even some l p spaces in this work we develop a theory of hardy and bmo spaces associated to l which includes in particular a molecular decomposition maximal and square function characterizations duality of hardy and bmo spaces and a john nirenberg inequality

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

differential geometry of curved exponential families curvatures and information loss the differential geometrical framework is given for analyzing statistical problems related to multi parameter families of distributions the dualistic structures of the exponential families and curved exponential families are elucidated from the geometrical viewpoint the duality connected by the legendre transformation is thus extended to include two kinds of affine connections and two kinds of curvatures the second order information loss is calculated for fisher efficient estimators and is decomposed into the sum of two non negative terms one is related to the exponential curvature of the statistical model and the other is related to the mixture curvature of the estimator only the latter term depends on the estimator and vanishes for the maximum likelihood estimator a set of statistics which recover the second order information loss are given the second order efficiency also is obtained the differential geometry of the function space of distributions is discussed

a comparison of asymptotically equivalent test statistics for regression transformation summary a simulation comparison is made of six asymptotically equivalent test statistics for transformation of the response in regression the tests typically have observed sizes up to twice the nominal size a likelihood ratio statistic a score statistic and a wald statistic behave very similarly both at the null hypothesis and in terms of power values of all the statistics are highly positively correlated the greater part of any differences between the statistics is concentrated in their standard deviations to test hypotheses about parametric families of transformation box cox 1964 use a likelihood ratio test more recently several other asymptotically equivalent tests have been suggested in the present paper we present empirical comparisons of six tests in terms of size power and diagnostic efficacy the interesting relevance of these results to small sample comparisons of score wald and likelihood ratio tests is briefly discussed the notation and background of the paper follow those of box cox 1964 a vector of n response values y is linearly related with an initial constant term to p 1 explanatory variables whose values and an initial column of ones are contained in an n xp matrix x the box cox family of transformations indexed by a scalar parameter a is employed to produce the transformed response variable y the aim is to choose a by maximum likelihood so that y follows the linear model y a x 3 e 1 1 where e is a vector of errors which are mutually independent with normal distributions of zero mean and constant variance a2 and 3 is a vector of coefficients the estimate a satisfies the equation

more on score tests for transformation in regression summary lawrance s 1987 results concerning tests for transformation in regression are extended to models where response and mean may both be transformed it is also suggested i that the methods of lawrance and of atkinson 1982 lead to statistics with near perfect correlation and ii that observed and expected informations may have considerably different effects as standardizations of the score statistic

hardy spaces and divergence operators on strongly lipschitz domains of rn abstract let be a strongly lipschitz domain of r n consider an elliptic second order divergence operator l including a boundary condition on and define a hardy space by imposing the non tangential maximal function of the extension of a function f via the poisson semigroup for l to be in l1 under suitable assumptions on l we identify this maximal hardy space with h 1 r n if r n with h r 1 under the dirichlet boundary condition and with h z 1 under the neumann boundary condition

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

likelihood and observed geometries a partir du point de vue de la conditionnalite on etablit un parallele observe a la theorie de chentsov efron amari etc en utilisant l information observee et un tenseur d asymetrie observee

new function spaces of bmo type the john nirenberg inequality interpolation and applications in this paper we introduce and develop some new function spaces of bmo bounded mean oscillation type on spaces of homogeneous type or measurable subsets of spaces of homogeneous type the new function spaces are defined by variants of maximal functions associated with generalized approximations to the identity and they generalize the classical bmo space we show that the john nirenberg inequality holds on these spaces and they interpolate with lp spaces by the complex interpolation method we then give applications on lp boundedness of singular integrals whose kernels do not satisfy the hormander condition 2005 wiley periodicals inc

self improving properties for abstract poincare type inequalities we study self improving properties in the scale of lebesgue spaces of generalized poincar e inequalities in the euclidean space we present an abstract setting where oscillations are given by certain operators e g approximations of the identity semigroups or mean value operators that have o diagonal decay in some range our results provide a unied theory that is applicable to the classical poincar e inequalities and furthermore it includes oscillations dened in terms of semigroups associated with second order elliptic operators as those in the kato conjecture in this latter situation we obtain a direct proof of the john nirenberg inequality for the associated bmo and lipschitz spaces of hmay hmm

extension of twisted hodge metrics for kahler morphisms let f x y be a holomorphic map of complex manifolds which is proper kahler and surjective with connected fibers and which is smooth over y z the complement of an analytic subset z let e be a nakano semi positive vector bundle on x and consider direct image sheaves f r qf k x y otimes e for q geq 0 in our previous paper we discussed the nakano semi positivity of f with respect to the so called hodge metric when the map f is smooth in this paper we discuss the extension of the induced metric on the tautological line bundle o 1 on the projective space bundle p f over y z as a singular hermitian metric with semi positive curvature over y as a particular consequence if y is projective r qf k x y otimes e is weakly positive over y z in the sense of viehweg