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June, 2004 Maximal and Fractional Operators in Weighted $L^{p(x)}$ Spaces
Vakhtang Kokilashvili, Stefan Samko
Rev. Mat. Iberoamericana 20(2): 493-515 (June, 2004).


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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Vakhtang Kokilashvili. Stefan Samko. "Maximal and Fractional Operators in Weighted $L^{p(x)}$ Spaces." Rev. Mat. Iberoamericana 20 (2) 493 - 515, June, 2004.


Published: June, 2004
First available in Project Euclid: 17 June 2004

zbMATH: 1099.42021
MathSciNet: MR2073129

Primary: 42B25 , 47B38

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

Rights: Copyright © 2004 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.20 • No. 2 • June, 2004
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