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

Ebner Pineda; Luz Rodriguez; Wilfredo Urbina; Ebner Pineda; Luz Rodriguez; Wilfredo Urbina

doi:10.3934/math.2025049

AIMS Mathematics

2025, Volume 10, Issue 1: 1026-1042. doi: 10.3934/math.2025049

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Research article

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

1.
Escuela Superior Politécnica del Litoral. ESPOL, FCNM, Campus Gustavo Galindo Km. 30.5 Vía Perimetral, P.O. Box 09-01-5863, Guayaquil, Ecuador
2.
Department of Mathematics, Actuarial Sciences and Economics, Roosevelt University, Chicago, IL, 60605, USA

Received: 29 September 2024 Revised: 13 December 2024 Accepted: 25 December 2024 Published: 17 January 2025
MSC : Primary 42B25, 42B35; Secondary 46E30, 47G10

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(\cdot), q(\cdot)}^{\alpha}(\gamma_{d}), $ which were defined and studied in ^[9], under certain conditions on $ p(\cdot) $ and $ q(\cdot) $.
- Bessel potential,
- fractional derivative,
- variable exponent,
- Besov$ - $Lipschitz,
- Gaussian measure
Citation: Ebner Pineda, Luz Rodriguez, Wilfredo Urbina. Boundedness of Gaussian Bessel potentials and fractional derivatives on variable Gaussian Besov$ - $Lipschitz spaces[J]. AIMS Mathematics, 2025, 10(1): 1026-1042. doi: 10.3934/math.2025049

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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(\cdot), q(\cdot)}^{\alpha}(\gamma_{d}), $ which were defined and studied in ^[9], under certain conditions on $ p(\cdot) $ and $ q(\cdot) $.

References

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