Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Variable order fractional integrals in variable generalized Hölder spaces of holomorphic functions

Variable order fractional integrals in variable generalized Hölder spaces of holomorphic functions We introduce and study the variable generalized Hölder spaces of holomorphic functions over the unit disc in the complex plane. These spaces are defined either directly in terms of modulus of continuity or in terms of estimates of derivatives near the boundary. We provide conditions of Zygmund type for imbedding of the former into the latter and vice versa. We study mapping properties of variable order fractional integrals in the frameworks of such spaces. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

Variable order fractional integrals in variable generalized Hölder spaces of holomorphic functions

Loading next page...
 
/lp/springer-journals/variable-order-fractional-integrals-in-variable-generalized-h-lder-BPiIBUuOOn
Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-021-00587-0
Publisher site
See Article on Publisher Site

Abstract

We introduce and study the variable generalized Hölder spaces of holomorphic functions over the unit disc in the complex plane. These spaces are defined either directly in terms of modulus of continuity or in terms of estimates of derivatives near the boundary. We provide conditions of Zygmund type for imbedding of the former into the latter and vice versa. We study mapping properties of variable order fractional integrals in the frameworks of such spaces.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Dec 1, 2021

Keywords: Hadamard–Bergman convolution operators; Hölder space of holomorphic functions; Fractional integro-differentiation; 47G10; 47B38; 46E30

References