scholarly journals Integral means on radially weighted spaces of analytic functions

1998 ◽  
Vol 65 (1) ◽  
pp. 68-83
Author(s):  
Mats Erik Andersson
Keyword(s):  
Analytic Functions ◽  
Weighted Sums ◽  
Complex Method ◽  
Integral Means ◽  
Rotationally Symmetric ◽  
Function Norm ◽  
Carry Over ◽  
Two Parameters ◽  
Spaces Of Analytic Functions ◽  
Domination Relation

AbstractHilbert spaces of analytic functions generated by rotationally symmetric measures on disks and annuli are studied. A domination relation between function norm and weighted sums of integral means on circles is developed. The function norm and the weighted sum take the same value for a specified class of polynomials. This class can be varied according to two parameters. Parts of the construction carry over to other Banach spaces of analytic of harmonic functions. Counterexamples illuminating properties of the complex method of interpolation appear as a byproduct.

scholarly journals Integration Operators in Average Radial Integrability Spaces of Analytic Functions

2021 ◽  
Vol 18 (3) ◽  
Author(s):  
Tanausú Aguilar-Hernández ◽  
Manuel D. Contreras ◽  
Luis Rodríguez-Piazza
Keyword(s):  
Analytic Functions ◽  
Spaces Of Analytic Functions

Some properties for certain subclasses of analytic functions defined by a general differential operator

2019 ◽  
Vol 13 (07) ◽  
pp. 2050134
Author(s):  
Erhan Deniz ◽  
Murat Çağlar ◽  
Yücel Özkan
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Partial Sums ◽  
Integral Means

In this paper, we study two new subclasses [Formula: see text] and [Formula: see text] of analytic functions which are defined by means of a differential operator. Some results connected to partial sums and neighborhoods and integral means related to these subclasses are obtained.

scholarly journals QKtype spaces of analytic functions

2006 ◽  
Vol 4 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Hasi Wulan ◽  
Jizhen Zhou
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Nondecreasing Function ◽  
Necessary And Sufficient Conditions ◽  
Type Space ◽  
Necessary And Sufficient ◽  
Spaces Of Analytic Functions

For a nondecreasing functionK:[0,8)?[0,8)and0<p<8,-2<q<8, we introduceQK(p,q), aQKtype space of functions analytic in the unit disk and study the characterizations ofQK(p,q). Necessary and sufficient conditions onKsuch thatQK(p,q)become some known spaces are given.

Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions

1999 ◽  
Vol 42 (2) ◽  
pp. 139-148 ◽  
Author(s):  
José Bonet ◽  
Paweł Dománski ◽  
Mikael Lindström
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Essential Norm ◽  
Weak Compactness ◽  
Weakly Compact ◽  
Point Evaluation ◽  
Weighted Banach Spaces ◽  
Spaces Of Analytic Functions

AbstractEvery weakly compact composition operator between weighted Banach spaces of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

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