TY - GEN

T1 - Fractional Operators from Vanishing Morrey to Vanishing Campanato Spaces in the Variable Exponent Setting on Quasi-metric Measure Spaces

AU - Rafeiro, Humberto

AU - Samko, Stefan

N1 - Funding Information:
Acknowledgements The research of H. Rafeiro was supported by a Start-up Grant of United Arab Emirates University, Al Ain, United Arab Emirates via Grant No. G00002994. The research of S. Samko was supported by: (a) Russian Foundation for Basic Research under the grant No. 19-01-00223, and (b) TUBITAK and Russian Foundation for Basic research under the grant No. 20-51-46003.
Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Campanato space

KW - Fractional operator

KW - Morrey space

KW - Quasi-metric measure space

UR - http://www.scopus.com/inward/record.url?scp=85140744827&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85140744827&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-06170-7_16

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

M3 - Conference contribution

AN - SCOPUS:85140744827

SN - 9783031061691

T3 - Springer Proceedings in Mathematics and Statistics

SP - 265

EP - 275

BT - Infinite Dimensional Analysis, Quantum Probability and Applications - QP41 Conference, 2021

A2 - Accardi, Luigi

A2 - Mukhamedov, Farrukh

A2 - Al Rawashdeh, Ahmed

PB - Springer

T2 - 41st International Conference on Quantum Probability and Related Topics, QP41 2021

Y2 - 28 March 2021 through 1 April 2021

ER -