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Hardy-Littlewood, Bessel-Riesz, and fractional integral operators in anisotropic Morrey and Campanato spaces
File(s)
Author(s)
Ruzhansky, Michael
Suragan, Durvudkhan
Yessirkegenov, Nurgissa
Type
Journal Article
Abstract
We analyse Morrey spaces, generalised Morrey spaces and Campanato spaces on homogeneous groups. The boundedness of the Hardy-Littlewood maximal operator, Bessel-Riesz operators, generalised Bessel-Riesz operators and generalised fractional integral operators in generalised Morrey spaces on homogeneous groups is shown. Moreover, we prove the boundedness of the modified version of the generalised fractional integral operator and Olsen type inequalities in Campanato spaces and generalised Morrey spaces on homogeneous groups, respectively. Our results extend results known in the isotropic Euclidean settings, however, some of them are new already in the standard Euclidean
cases.
Date Issued
2018-06-26
Date Acceptance
2018-04-18
Citation
Fractional Calculus and Applied Analysis, 2018, 21 (3), pp.577-612
URI
DOI
ISSN
1311-0454
Publisher
De Gruyter
Start Page
577
End Page
612
Journal / Book Title
Fractional Calculus and Applied Analysis
Volume
21
Issue
3
Copyright Statement
© 2018 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0 ( http://creativecommons.org/licenses/by-nc-nd/3.0 )
Subjects
math.FA
math.FA
Notes
29 pages
Publication Status
Published
Date Publish Online
2018-07-12