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

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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