Boundedness of Gaussian Bessel Potentials and Bessel Fractional Derivatives on variable Gaussian Besov-Lipschitz spaces

TL;DR

This paper investigates the regularity properties of Gaussian Bessel potentials and fractional derivatives within variable Gaussian Besov-Lipschitz spaces, extending understanding of their boundedness under specific variable exponent conditions.

Contribution

It establishes boundedness results for Gaussian Bessel potentials and derivatives on variable Gaussian Besov-Lipschitz spaces, advancing the theory of function spaces with variable exponents.

Findings

Boundedness of Gaussian Bessel potentials on variable spaces

Boundedness of Gaussian Bessel fractional derivatives on variable spaces

Extension of regularity properties to variable exponent settings

Abstract

In this paper we study the regularity properties of the Gaussian Bessel potentials and Gaussian Bessel fractional derivatives on variable Gaussian Besov-Lipschitz spaces $B_{p(\cdot),q(\cdot)}^{\alpha}(\gamma_{d}),$ that were defined in a previous paper \cite{Pinrodurb}, under certain conditions on $p(\cdot)$ and $q(\cdot)$.