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Research Article | Open Access

Boundedness of Gaussian Bessel potentials and fractional derivatives on variable Gaussian Besov −Lipschitz spaces

Ebner Pineda1( ), Luz Rodriguez1, Wilfredo Urbina2
Escuela Superior Politécnica del Litoral. ESPOL, FCNM, Campus Gustavo Galindo Km. 30.5 Vía Perimetral, P.O. Box 09-01-5863, Guayaquil, Ecuador
Department of Mathematics, Actuarial Sciences and Economics, Roosevelt University, Chicago, IL, 60605, USA
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Abstract

In this paper, following [6], we study the regularity properties of Bessel potentials and Bessel fractional derivatives in the context of variable Gaussian Besov −Lipschitz spaces B p ( ⋅ ) , q ( ⋅ ) α ( γ d ) , which were defined and studied in [9], under certain conditions on p ( ⋅ ) and q ( ⋅ ).

Keywords

Bessel potentialfractional derivativevariable exponentBesov−LipschitzGaussian measure
CLC number: Primary 42B25, 42B35; Secondary 46E30, 47G10

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AIMS Mathematics
Volume 10 Issue 1,
January 2025
Pages 1026-1042
DOI: 10.3934/math.2025049

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Pineda E, Rodriguez L, Urbina W. Boundedness of Gaussian Bessel potentials and fractional derivatives on variable Gaussian Besov −Lipschitz spaces. AIMS Mathematics, 2025, 10(1): 1026-1042. https://doi.org/10.3934/math.2025049

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Received: 29 September 2024
Revised: 13 December 2024
Accepted: 25 December 2024
Published: 15 January 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)