Fractional Operators from Vanishing Morrey to Vanishing Campanato Spaces in the Variable Exponent Setting on Quasi-metric Measure Spaces

Humberto Rafeiro, Stefan Samko

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In the framework of bounded quasi-metric measure spaces (X, d, μ), we prove that the fractional operator of variable order α(x) is bounded from vanishing variable exponent Morrey space VLp(·),λ(·)(X) to vanishing variable exponent Campanato space, when γ⩽ α(x) p(x) + λ(x) ⩽ γ+ θp(x). We do not assumed that the space (X, d, μ) is homogeneous and impose only the growth condition μB(x, r) ⩽ Crγ on the measure and suppose that the distance is θ -regular in the sense of R. Macías and C. Segovia.

Original languageEnglish
Title of host publicationInfinite Dimensional Analysis, Quantum Probability and Applications - QP41 Conference, 2021
EditorsLuigi Accardi, Farrukh Mukhamedov, Ahmed Al Rawashdeh
PublisherSpringer
Pages265-275
Number of pages11
ISBN (Print)9783031061691
DOIs
Publication statusPublished - 2022
Event41st International Conference on Quantum Probability and Related Topics, QP41 2021 - Al Ain, United Arab Emirates
Duration: Mar 28 2021Apr 1 2021

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume390
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference41st International Conference on Quantum Probability and Related Topics, QP41 2021
Country/TerritoryUnited Arab Emirates
CityAl Ain
Period3/28/214/1/21

Keywords

  • Campanato space
  • Fractional operator
  • Morrey space
  • Quasi-metric measure space

ASJC Scopus subject areas

  • Mathematics(all)

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