scholarly journals On some spaces of holomorphic functions of exponential growth on a half-plane

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Marco M. Peloso ◽  
Maura Salvatori
Keyword(s):  
Half Plane ◽  
Exponential Growth ◽  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions ◽  
The Right

AbstractIn this paper we study spaces of holomorphic functions on the right half-plane R, that we denote by M

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.

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 Properties of Certain Classes of Holomorphic Functions Related to Strongly Janowski Type Function

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Bushra Kanwal ◽  
Khalida Inayat Noor ◽  
Saqib Hussain
Keyword(s):  
Growth Rate ◽  
Half Plane ◽  
Unit Disc ◽  
Univalent Functions ◽  
Holomorphic Functions ◽  
Circular Domain ◽  
Open Unit ◽  
Open Unit Disc ◽  
Inclusion Relations ◽  
The Right

Most subclasses of univalent functions are characterized with functions that map open unit disc ∇ onto the right-half plane. This concept was later modified in the literature with those mappings that conformally map ∇ onto a circular domain. Many researchers were inspired with this modification, and as such, several articles were written in this direction. On this note, we further modify this idea by relating certain subclasses of univalent functions with those that map ∇ onto a sector in the circular domain. As a result, conditions for univalence, radius results, growth rate, and several inclusion relations are obtained for these novel classes. Overall, many consequences of findings show the validity of our investigation.

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