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

Humberto Rafeiro; Stefan Samko

doi:10.1007/978-3-031-06170-7_16

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

Humberto Rafeiro, Stefan Samko

Department of Mathematical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference 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) ⩽ Cr^γ on the measure and suppose that the distance is θ -regular in the sense of R. Macías and C. Segovia.

Original language	English
Title of host publication	Infinite Dimensional Analysis, Quantum Probability and Applications - QP41 Conference, 2021
Editors	Luigi Accardi, Farrukh Mukhamedov, Ahmed Al Rawashdeh
Publisher	Springer
Pages	265-275
Number of pages	11
ISBN (Print)	9783031061691
DOIs	https://doi.org/10.1007/978-3-031-06170-7_16
Publication status	Published - 2022
Event	41st International Conference on Quantum Probability and Related Topics, QP41 2021 - Al Ain, United Arab Emirates Duration: Mar 28 2021 → Apr 1 2021

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	390
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	41st International Conference on Quantum Probability and Related Topics, QP41 2021
Country/Territory	United Arab Emirates
City	Al Ain
Period	3/28/21 → 4/1/21

Keywords

Campanato space
Fractional operator
Morrey space
Quasi-metric measure space

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-031-06170-7_16

Cite this

Rafeiro, H., & Samko, S. (2022). Fractional Operators from Vanishing Morrey to Vanishing Campanato Spaces in the Variable Exponent Setting on Quasi-metric Measure Spaces. In L. Accardi, F. Mukhamedov, & A. Al Rawashdeh (Eds.), Infinite Dimensional Analysis, Quantum Probability and Applications - QP41 Conference, 2021 (pp. 265-275). (Springer Proceedings in Mathematics and Statistics; Vol. 390). Springer. https://doi.org/10.1007/978-3-031-06170-7_16

Fractional Operators from Vanishing Morrey to Vanishing Campanato Spaces in the Variable Exponent Setting on Quasi-metric Measure Spaces. / Rafeiro, Humberto; Samko, Stefan.
Infinite Dimensional Analysis, Quantum Probability and Applications - QP41 Conference, 2021. ed. / Luigi Accardi; Farrukh Mukhamedov; Ahmed Al Rawashdeh. Springer, 2022. p. 265-275 (Springer Proceedings in Mathematics and Statistics; Vol. 390).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Rafeiro, H & Samko, S 2022, Fractional Operators from Vanishing Morrey to Vanishing Campanato Spaces in the Variable Exponent Setting on Quasi-metric Measure Spaces. in L Accardi, F Mukhamedov & A Al Rawashdeh (eds), Infinite Dimensional Analysis, Quantum Probability and Applications - QP41 Conference, 2021. Springer Proceedings in Mathematics and Statistics, vol. 390, Springer, pp. 265-275, 41st International Conference on Quantum Probability and Related Topics, QP41 2021, Al Ain, United Arab Emirates, 3/28/21. https://doi.org/10.1007/978-3-031-06170-7_16

Rafeiro H, Samko S. Fractional Operators from Vanishing Morrey to Vanishing Campanato Spaces in the Variable Exponent Setting on Quasi-metric Measure Spaces. In Accardi L, Mukhamedov F, Al Rawashdeh A, editors, Infinite Dimensional Analysis, Quantum Probability and Applications - QP41 Conference, 2021. Springer. 2022. p. 265-275. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-031-06170-7_16

Rafeiro, Humberto ; Samko, Stefan. / Fractional Operators from Vanishing Morrey to Vanishing Campanato Spaces in the Variable Exponent Setting on Quasi-metric Measure Spaces. Infinite Dimensional Analysis, Quantum Probability and Applications - QP41 Conference, 2021. editor / Luigi Accardi ; Farrukh Mukhamedov ; Ahmed Al Rawashdeh. Springer, 2022. pp. 265-275 (Springer Proceedings in Mathematics and Statistics).

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