JournalsrmiVol. 20, No. 2pp. 493–515

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

  • Vakhtang Kokilashvili

    Georgian Acadademy of Sciences, Tbilisi, Georgia
  • Stefan Samko

    University of Algarve, Faro, Portugal
Maximal and Fractional Operators in Weighted $L^{p(x)}$ Spaces cover
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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 Lp()(ρ,Ω)L^{p(\cdot)}(\rho,\Omega) over a bounded open set in Rn\mathbb{R}^n with a power weight ρ(x)=xx0γ\rho(x)=|x-x_0|^\gamma, x0Ωx_0\in \overline{\Omega}, and an exponent p(x)p(x) satisfying the Dini-Lipschitz condition.

Cite this article

Vakhtang Kokilashvili, Stefan Samko, Maximal and Fractional Operators in Weighted Lp(x)L^{p(x)} Spaces. Rev. Mat. Iberoam. 20 (2004), no. 2, pp. 493–515

DOI 10.4171/RMI/398