Maximal and Fractional Operators in Weighted $L^{p(x)}$ Spaces

Maximal and Fractional Operators in Weighted $L^{p(x)}$ Spaces

Vakhtang Kokilashvili and Stefan Samko

Source: Rev. Mat. Iberoamericana Volume 20, Number 2 (2004), 493-515.

Abstract

We study the boundedness of the maximal operator, potential type operators and operators with fixed singularity (of Hardy and Hankel type) in the spaces $L^{p(\cdot)}(\rho,\Omega)$ over a bounded open set in $\mathbb{R}^n$ with a power weight $\rho(x)=|x-x_0|^\gamma$, $x_0\in \overline{\Omega}$, and an exponent $p(x)$ satisfying the Dini-Lipschitz condition.

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Primary Subjects: 42B25, 47B38

Keywords: maximal functions; weighted Lebesgue spaces; variable exponent; potential operators; integral operators with fixed singularity

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.rmi/1087482024
Zentralblatt MATH identifier: 02110196
Mathematical Reviews number (MathSciNet): MR2073129

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