Continuous projections, duality, and the diagonal mapping in weighted spaces of holomorphic functions with mixed norm

2000 ◽  
Vol 101 (3) ◽  
pp. 3211-3215 ◽  
Author(s):  
F. A. Shamoyan ◽  
O. V. Yaroslavtseva
Keyword(s):  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Mixed Norm ◽  
Spaces Of Holomorphic Functions ◽  
Diagonal Mapping

scholarly journals Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions

2019 ◽  
Vol 277 (12) ◽  
pp. 108282 ◽  
Author(s):  
Karlheinz Gröchenig ◽  
Antti Haimi ◽  
Joaquim Ortega-Cerdà ◽  
José Luis Romero
Keyword(s):  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Spaces Of Holomorphic Functions

Composition operators on weighted spaces of holomorphic functions on the upper half plane

2018 ◽  
Vol 122 (1) ◽  
pp. 141
Author(s):  
Wolfgang Lusky
Keyword(s):  
Half Plane ◽  
Composition Operator ◽  
Unit Disc ◽  
Composition Operators ◽  
Bounded Operator ◽  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Weight Functions ◽  
Spaces Of Holomorphic Functions ◽  
Upper Half Plane

We consider moderately growing weight functions $v$ on the upper half plane $\mathbb G$ called normal weights which include the examples $(\mathrm{Im} w)^a$, $w \in \mathbb G$, for fixed $a > 0$. In contrast to the comparable, well-studied situation of normal weights on the unit disc here there are always unbounded composition operators $C_{\varphi }$ on the weighted spaces $Hv(\mathbb G)$. We characterize those holomorphic functions $\varphi \colon \mathbb G \rightarrow \mathbb G$ where the composition operator $C_{\varphi } $ is a bounded operator $Hv(\mathbb G) \rightarrow Hv(\mathbb G)$ by a simple property which depends only on $\varphi $ but not on $v$. Moreover we show that there are no compact composition operators $C_{\varphi }$ on $Hv(\mathbb G)$.

scholarly journals Bloch spaces of holomorphic functions in the polydisk

2007 ◽  
Vol 5 (3) ◽  
pp. 213-230 ◽  
Author(s):  
Anahit Harutyunyan
Keyword(s):  
Holomorphic Functions ◽  
Bloch Spaces ◽  
Spaces Of Holomorphic Functions ◽  
Diagonal Mapping ◽  
Anisotropic Spaces

This work is an introduction to anisotropic spaces of holomorphic functions, which haveω-weight and are generalizations of Bloch spaces to a polydisc. We prove that these classes form an algebra and are invariant with respect to monomial multiplication. Some theorems on projection and diagonal mapping are proved. We establish a description of(Ap(ω))*(or(Hp(ω))*via the Bloch classes for all0<p≤1.

scholarly journals Weighted Iterated Radial Composition Operators between Some Spaces of Holomorphic Functions on the Unit Ball

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Composition Operators ◽  
Holomorphic Functions ◽  
Mixed Norm ◽  
Mixed Norm Space ◽  
Type Space ◽  
Spaces Of Holomorphic Functions ◽  
Schmidt Norm ◽  
Norm Space ◽  
Weighted Type

The boundedness and compactness of weighted iterated radial composition operators from the mixed-norm space to the weighted-type space and the little weighted-type space on the unit ball are characterized here. We also calculate the Hilbert-Schmidt norm of the operator on the weighted Bergman-Hilbert space as well as on the Hardy space.

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