Revista Matemática Iberoamericana

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Volume 20, Issue 2, 2004, pp. 493–515
DOI: 10.4171/RMI/398

Published online: 2004-08-31

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

Vakhtang Kokilashvili[1] and Stefan Samko[2]

(1) Georgian Acadademy of Sciences, Tbilisi, Georgia
(2) University of Algarve, Faro, Portugal

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.

Keywords: Maximal functions, weighted Lebesgue spaces, variable exponent, potential operators, integral operators with fixed singularity

Kokilashvili Vakhtang, Samko Stefan: Maximal and Fractional Operators in Weighted $L^{p(x)}$ Spaces. Rev. Mat. Iberoam. 20 (2004), 493-515. doi: 10.4171/RMI/398