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- Title
EMBEDDINGS AND RELATED TOPICS IN GRAND VARIABLE EXPONENT HAJŁASZ–MORREY–SOBOLEV SPACES.
- Authors
EDMUNDS, DAVID E.; MAKHARADZE, DALI; MESKHI, ALEXANDER
- Abstract
Embeddings in the framework of grand variable exponent function spaces are studied. In particular, embeddings from grand variable exponent Hajłasz-Sobolev-Morrey spaces to variable exponent H ¨older spaces are established. The regularity of a fractional integral operator defined with respect to a non-doubling measure is also investigated. In particular, mapping properties of this operator from a grand variable exponent Morrey space to a grand variable parameter H ¨older space are studied. The results are proved under the log-H ¨older continuity condition on the exponents. The spaces are defined, generally speaking, on quasi-metric measure spaces, however, the results are new even for Euclidean spaces.
- Subjects
QUASI-metric spaces; EXPONENTS; FRACTIONAL integrals; FUNCTION spaces
- Publication
Mathematical Inequalities & Applications, 2024, Vol 27, Issue 1, p201
- ISSN
1331-4343
- Publication type
Article
- DOI
10.7153/mia-2024-27-16