Maximal and Fractional Operators in Weighted Lᵖ⁽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 Lp(·)(ρ,Ω) over a bounded open set in R^n with a power weight ρ(x)=|x-x_0|^γ , x_0∈ Ω̄ , and an exponent p(x) satisfying the Dini-Lipschitz condition.