composition operators from bloch type spaces to hardy and besov spaces boundedness and compactness of composition operators from bloch type spaces to hardy spaces and analytic besov spaces are characterized by function theoretic properties of their inducing maps for the case of the bloch space the characterizations involve the hyperbolic versions of hardy and besov classes the conditions for the hyperbolic besov classes are then interpreted geometrically when the symbols are univalent and strict inclusion between different hyperbolic besov classes is shown by an example

extremal solutions of measure differential equations abstract we investigate the existence of the least and greatest solutions to measure differential equations as well as the relation between the extremal solutions and lower or upper solutions along the way we prove a fairly general local existence theorem and an analogue of peano s uniqueness theorem for measure differential equations finally we show that the general theory is applicable in the study of differential equations with impulses or dynamic equations on time scales

on the diffeomorphism types of certain algebraic surfaces i l invariant de donaldson la geometrie de certaines surfaces rationnelles surfaces dolgachev generalites sur des formes de type 1 n la classe canonique d une chambre et un coin le cone de kahler d une bonne surface generique une etude de p cellules les super p cellules

on the solvability of distributional and impulsive systems of cauchy problems abstract in this paper existence results are derived for the unique smallest greatest minimal and or maximal solutions of finite systems of nonlinear distributional cauchy problems the dependence of solutions on the data is also studied applications to systems of distributional differential equations with impulses and to higher order distributional cauchy problems are presented the main tools are fixed point results in function spaces and a primitive integral of distributions defined in the paper including recently introduced regulated and continuous primitive integrals on compact intervals

compact and weakly compact composition operators from the bloch space into mobius invariant spaces we obtain exhaustive results and treat in a unified way the question of boundedness compactness and weak compactness of composition operators from the bloch space into any space from a large family of conformally invariant spaces that includes the classical spaces like bmoa q and analytic besov spaces bp in particular by combining techniques from both complex and functional analysis we prove that in this setting weak compactness is equivalent to compactness for the operators into the corresponding small spaces we also characterize the boundedness and show that it is equivalent to compactness

essential norm of products of multiplication composition and differentiation operators on weighted bergman spaces abstract let be a holomorphic function on the open unit disk d and a holomorphic self map of d let c m and d denote the composition multiplication and differentiation operator respectively we find an asymptotic expression for the essential norm of products of these operators on weighted bergman spaces on the unit disk this paper is a continuation of our recent paper concerning the boundedness of these operators on weighted bergman spaces

hyperbolic mean growth of bounded holomorphic functions in the ball we consider the hyperbolic hardy class q h p b 0 p it consists of holomorphic in the unit complex ball b for which 1 and sup q r 0 p d 0 r 1 b where q denotes the hyperbolic distance of the unit disc the hyperbolic version of the littlewood paley type g function and the area function are defined in terms of the invariant gradient of b and membership of qh p b is expressed by the l p property of the functions as an application we can characterize the boundedness and the compactness of the composition operator c defined by c f f o from the bloch space into the hardy space h p b

composition type operator from bergman space to μ bloch type space in cn abstract let be a holomorphic self map of b and h b a composition type operator t is defined by t f f we can regard this operator as a generalization of a multiplication operator and a composition operator for normal functions some necessary and sufficient conditions are given for which t is a bounded or compact operator from bergman space to bloch type space on the unit ball of c n as a corollary we obtain the pointwise multiplier from bergman space to bloch type space on b

well posedness results for abstract generalized differential equations and measure functional differential equations abstract in the first part of the paper we consider nonlinear generalized ordinary differential equations whose solutions take values in infinite dimensional banach spaces and prove new theorems concerning the existence of solutions and continuous dependence on initial values and parameters in the second part we apply these results in the study of nonlinear measure functional differential equations and impulsive functional differential equations with infinite delay

on nonlinear distributional and impulsive cauchy problems abstract in this paper existence results are derived for the unique smallest greatest minimal and maximal solutions of nonlinear distributional cauchy problems dependence of solutions on the data is also studied the obtained results are applied to impulsive differential equations main tools are fixed point results in function spaces and recently introduced concepts of regulated and continuous primitive integrals of distributions

compact composition operators on the bloch space necessary and sufficient conditions are given for a composition operator cof f o q to be compact on the bloch space w and on the little bloch space o weakly compact composition operators on o are shown to be compact if q e o is a conformal mapping of the unit disk d into itself whose image q d approaches the unit circle t only in a finite number of nontangential cusps then co is compact on 7o on the other hand if there is a point of t n q d at which q d does not have a cusp then co is not compact

products of multiplication composition and differentiation operators on weighted bergman spaces abstract let be a holomorphic function on the open unit disk d and a holomorphic self map of d let c m and d denote the composition multiplication and differentiation operator respectively we consider linear operators induced by products of these operators on weighted bergman spaces on d the boundedness is established by using carleson type measures

weighted composition operators between weighted bergman spaces and hardy spaces on the unit ball of cn abstract in this paper we study the weighted composition operators w f f between weighted bergman spaces and hardy spaces on the unit ball of c n we characterize the boundedness and the compactness of the weighted composition operators w a p a q 0 q p 1 and w h p b h q b 0 q p

the orientation of yang mills moduli spaces and 4 manifold topology si x est une 4 variete lisse orientee fermee dont la forme intersection q h 2 x z torsion z est definie negative alors la forme est equivalente sur les entiers a la forme standard 1 1 1 soit x une 4 variete lisse orientee fermee avec les trois proprietes suivantes 1 h 1 x z n a pas de 2 torsion 2 la forme intersection q sur h 2 x torsion a une partie positive de rang 1 ou 2 3 la forme intersection est paire alors q est equivalente sur les entiers a une des formes 01 10 01 10 01 10

rigidity of composition operators on the hardy space h p abstract let be an analytic map taking the unit disk d into itself we establish that the class of composition operators f c f f exhibits a rather strong rigidity of non compact behaviour on the hardy space h p for 1 p and p 2 our main result is the following trichotomy which states that exactly one of the following alternatives holds i c is a compact operator h p h p ii c fixes a linearly isomorphic copy of l p in h p but c does not fix any copies of l 2 in h p iii c fixes a copy of l 2 in h p moreover in case iii the operator c actually fixes a copy of l p 0 1 in h p provided p 1 we reinterpret these results in terms of norm closed ideals of the bounded linear operators on h p which contain the compact operators k h p in particular the class of composition operators on h p does not reflect the quite complicated lattice structure of such ideals

composition operators between bergman and hardy spaces we study composition operators between weighted bergman spaces certain growth conditions for generalized nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact particular choices for the weights yield results on composition operators between the classical unweighted bergman and hardy spaces

on norms of composition operators acting on bergman spaces for arbitrary composition operators acting on a general bergman space we improve the known lower bound for the norm and also generalize a related recent theorem of d g pokorny and j e shapiro next we obtain a geometric formula for the norms of composition operators with linear fractional symbols thus extending a result of c cowen and p hurst and revealing the meaning of their computation finally we obtain a lower bound for essential norm of an arbitrary composition operator related to the well known criterion of b maccluer and j h shapiro as a corollary norms and essential norms are obtained for certain univalently induced noncompact composition operators in terms of the minimum of the angular derivative of the symbol

composition operators acting on holomorphic sobolev spaces we study the action of composition operators on sobolev spaces of analytic functions having fractional derivatives in some weighted bergman space or hardy space on the unit disk criteria for when such operators are bounded or compact are given in particular we find the precise range of orders of fractional derivatives for which all composition operators are bounded on such spaces sharp results about boundedness and compactness of a composition operator are also given when the inducing map is polygonal