scholarly journals Two Equivalent Presentations for the Norm of Weighted Spaces of Holomorphic Functions on the Upper Half-plane

2019 ◽  
Vol 5 (1) ◽  
pp. 1-8
Author(s):  
ma ardalani ◽  
Keyword(s):  
Half Plane ◽  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Spaces Of Holomorphic Functions ◽  
Upper Half Plane

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 $Hv(\mathbb G)$.

Isometries of weighted spaces of holomorphic functions on unbounded domains

2009 ◽  
Vol 139 (2) ◽  
pp. 253-271 ◽  
Author(s):  
Christopher Boyd ◽  
Pilar Rueda
Keyword(s):  
Half Plane ◽  
Complex Plane ◽  
Unbounded Domains ◽  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Bounded Domains ◽  
Spaces Of Holomorphic Functions ◽  
The Right

We study isometries between weighted spaces of holomorphic functions on unbounded domains in ℂn. We show that weighted spaces of holomorphic functions on unbounded domains may exhibit behaviour different from that observed on bounded domains. We calculate the isometries for specific weights on the complex plane and the right half-plane.

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
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