Mixed norm spaces of analytic functions as spaces of generalized fractional derivatives of functions in Hardy type spaces-Reference-Cited by-同舟云学术

Mixed norm spaces of analytic functions as spaces of generalized fractional derivatives of functions in Hardy type spaces

Published:2017-10-01 Issue:5 Volume:20 Page:1106-1130
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Karapetyants Alexey¹²,Samko Stefan³

Affiliation:

1. Southern Federal University Mathematics , Mechanics and Computer Sciences Department Miltchakova, 8a , Rostov-on-Don , 344090 – Russia

2. Don State Technical University , Rostov-on-Don , Russia

3. University of Algarve , Departamento de Matemática Campus de Gambelas, 8005–139 Faro , Portugal

Abstract

Abstract The aim of the paper is twofold. First, we present a new general approach to the definition of a class of mixed norm spaces of analytic functions 𝓐 q;X (𝔻), 1 ⩽ q < ∞ on the unit disc 𝔻. We study a problem of boundedness of Bergman projection in this general setting. Second, we apply this general approach for the new concrete cases when X is either Orlicz space or generalized Morrey space, or generalized complementary Morrey space. In general, such introduced spaces are the spaces of functions which are in a sense the generalized Hadamard type derivatives of analytic functions having lq summable Taylor coefficients.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2017-0059/pdf

Reference40 articles.

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