weighted iterated radial operators between different weighted bergman spaces on the unit ball abstract the boundedness and compactness of weighted iterated radial operators between different weighted bergman spaces on the unit ball are characterized here

norm and essential norm of composition followed by differentiation from α bloch spaces to hμ abstract this note calculates the norm of composition followed by differentiation operator from the bloch and the little bloch space to the weighted space h on the unit disk and gives an upper and a lower bound for the essential norm of the operator from the bloch space b 0 to h

composition operators from the space of cauchy transforms to bloch and the little bloch type spaces on the unit disk abstract we completely characterize the boundedness and compactness of composition operators from the space of cauchy transforms on the unit disk d into the bloch type space b as well as the little bloch type space b 0 consisting respectively of all holomorphic functions f on d such that sup z d z f z that is of all holomorphic functions f on d such that lim z 1 z f z 0 for some weight function as a byproduct of our results norm of the operator is calculated when b is replaced by b c

on operator p g φ from the logarithmic bloch type space to the mixed norm space on the unit ball the boundedness and compactness of the following recently introduced by this author integral type operatorp f gf z email protected 0 1f f tz g tz dtt email protected b where f is a holomorphic self map of the unit ball b in c n and g is a holomorphic function on b such that g 0 0 from logarithmic bloch type spaces to mixed norm spaces on b are studied in this paper

minimization problem associated with an improved hardy sobolev type inequality abstract we consider the existence or non existence of a minimizer of the following minimization problems associated with an improved hardy sobolev type inequality introduced by ioku 2019 i a inf u w 0 1 p b r 0 b r u p d x b r u p s v a x d x p p s where v a x 1 x s 1 a x r n p p 1 1 x s where 1 p n and 0 s p the minimization problem i a is equivalent to the minimization problem associated with the classical hardy sobolev inequality on r n via a transformation if we restrict ourselves to radial functions in contrast to the classical results for a 0 we show the existence of non radial minimizers for the hardy sobolev critical exponent p s p n s n p on bounded domains furthermore as an application of the transformation we derive an infinite dimensional form of the classical sobolev inequality in some sense

products of volterra type operator and composition operator from h and bloch spaces to zygmund spaces the boundedness and compactness of the products of volterra type operators and composition operators from the space of bounded analytic functions and the bloch space to the zygmund space are discussed in this paper

products of integral type operators and composition operators between bloch type spaces a complete picture on the boundedness and compactness of the products of integral type operators and composition operators between bloch type spaces of holomorphic functions on the unit disk is given in this paper

products of composition and differentiation operators from zygmund spaces to bloch spaces and bers spaces abstract the boundedness and compactness of the products of differentiation and composition operators from zygmund spaces to bloch spaces and bers spaces are discussed in this paper

generalized composition operators on zygmund spaces and bloch type spaces the boundedness and compactness of the generalized composition operator on zygmund spaces and bloch type spaces are investigated in this paper

on a new integral type operator from the bloch space to bloch type spaces on the unit ball abstract we introduce the following integral type operator on the space h b of all holomorphic functions on the unit ball b c n p g f z 0 1 f t z g t z d t t z b where g h b g 0 0 and is a holomorphic self map of b the boundedness and compactness of the operator from the bloch space b or the little bloch space b 0 to the bloch type space b or the little bloch type space b 0 are characterized in the main results we calculate the essential norm of the operators p g b or b 0 b or b 0 in an elegant way

weighted differentiation composition operators from h and bloch spaces to nth weighted type spaces on the unit disk we characterize the boundedness and compactness of weighted differentiation composition operators from the space of bounded analytic functions the bloch space and the little bloch space to nth weighted type spaces on the unit disk

on an integral type operator from logarithmic bloch type spaces to mixed norm spaces on the unit ball let h b denote the space of all holomorphic functions on the open unit ball b of c n and email protected h b we characterize the boundedness and compactness of the following integral type operator l gf z email protected 0 1rf tz g tz dtt email protected b where rf is the radial derivative of function f from logarithmic bloch type spaces to mixed norm spaces on the unit ball

the heat equation with a singular potential of concern is the singular problem du dt au c x 2 iz x tz x 0 u0 x and its generalizations here c 0 x g rn t 0 and and t 0 are nonnegative and not both identically zero there is a dimension dependent constant c n such that the problem has no solution for c ct n for c s ct a necessary and sufficient conditions are found for and u0 so that a nonnegative solution exists

c1 α local regularity of weak solutions of degenerate elliptic equations abstract it is demonstrated the local c 1 alpha nature of weak solutions of elliptic equations of the type 1 1 in the introduction under the degeneracy or singularity assumptions a sub 1 a sub 3

characterizations of composition followed by differentiation between bloch type spaces abstract some results on the boundedness and compactness of composition followed by differentiation between bloch type spaces are refined in this paper

integral type operators between α bloch spaces and besov spaces on the unit ball abstract let h b denote the space of all holomorphic functions on the unit ball b c n the boundedness and compactness of the following integral type operators t g f z 0 1 f tz r g tz dt t and l g f z 0 1 r f tz g tz dt t z b where g h b and r h z is the radial derivative of h between bloch spaces and besov spaces on the unit ball are characterized the results regarding the case when these operators map bloch spaces to besov spaces are nontrivial generalizations of recent one dimensional results by li and the present author

minimizers of caffarelli kohn nirenberg inequalities with the singularity on the boundary let be a bounded smooth domain in bf r n n geqq 3 and d a 1 2 omega be the completion of c 0 infty omega with respect to the norm u a 2 int omega x 2a nabla u 2 d x the caffarelli kohn nirenberg inequalities state that there is a constant c 0 such that begin array ll int omega x bq u q d x frac 2 q leqq c int omega x 2a nabla u 2 d x end array quad quad 0 1 for u in d a 1 2 omega and infty a frac n 2 2 quad 0 leqq b a leqq 1 quad q frac 2n n 2 2 b a we prove the best constant for 0 1 s a b omega inf limits u in d a 1 2 backslash 0 frac int omega x 2a nabla u 2 d x int omega x bq u q d x frac 2 q is always achieved in d a 1 2 omega provided that 0 in partial omega and the mean curvature h 0 0 where a b satisfies i a 0 rm and n geqq 4 if a 0 and 1 b 0 then the result was proved by ghoussoub and robert 12

weighted differentiation composition operators from mixed norm spaces to weighted type spaces motivated by the recent paper x zhu products of differentiation composition and multiplication from bergman type spaces to bers spaces integral transform spec funct 18 3 2007 223 231 we study the boundedness and compactness of the weighted differentiation composition operator d f u n f z u z f n f z where u is a holomorphic function on the unit disk d f is a holomorphic self map of d and email protected n 0 from the mixed norm space h p q f where p q 0 and f is normal to the weighted type space h m or the little weighted type space h m 0 for the case of the weighted bergman space a a p p 1 some bounds for the essential norm of the operator are also given

generalized composition operators from f p q s spaces to bloch type spaces abstract let h b denote the space of all holomorphic functions on the unit ball b of c n let be a holomorphic self map of b and g h b such that g 0 0 in this paper we investigate the boundedness and compactness of the generalized composition operator c g f z 0 1 r f tz g tz dt t which map from f p q s and f0 p q s to bloch type space b in the unit ball

a unified approach to improved l p hardy inequalities with best constants we present a unified approach to improved l p hardy inequalities in r n we consider hardy potentials that involve either the distance from a point or the distance from the boundary or even the intermediate case where the distance is taken from a surface of codimension 1 k n in our main result we add to the right hand side of the classical hardy inequality a weighted l p norm with optimal weight and best constant we also prove nonhomogeneous improved hardy inequalities where the right hand side involves weighted l q norms q p

on an integral type operator between bloch type spaces let h b denote the space of all holomorphic functions on the unit ball b of c n let f be a holomorphic self map of b and email protected h b such that g 0 0 we study the boundedness and compactness of the following integral type operator recently introduced by stevicp f g f z email protected 0 1f f tz g tz dtt email protected b between bloch type spaces our main results are natural extensions of some results in the following paper s stevic on a new integral type operator from the bloch space to bloch type spaces on the unit ball j math anal appl 354 2009 426 434

extremal functions of generalized critical hardy inequalities abstract in this paper we show the existence and non existence of minimizers of the following minimization problems which include an open problem mentioned by horiuchi and kumlin 20 g a inf u w 0 1 n 0 u n d x u q f a x d x n q where f a x x n log a r x first we give an answer to the open problem when b r 0 next we investigate the minimization problems on general bounded domains in this case the results depend on the shape of the domain finally symmetry breaking property of the minimizers is proved for sufficiently large

composition followed by differentiation from h and the bloch space to nth weighted type spaces on the unit disk the boundedness and compactness of the product of the differentiation and composition operator from the space of bounded analytic functions the bloch space and the little bloch space to nth weighted type spaces on the unit disk are characterized

existence and non existence of the first eigenvalue of the perturbed hardy sobolev operator in this paper we study the existence non existence and simplicity of the rst eigenvalue of the perturbed hardy sobolev operator i i 1 4 n i2 2 q jxj2 under various assumptions on the perturbation q we study the asymptotic behaviour of the rst eigenfunction near the origin when the perturbation q is q s 0 s 1 we will also establish the best constant in a hardy sobolev inequality proved by adimurthi e t a l

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