Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators

We prove Sobolev-type p(·)→q(·)-theorems for the Riesz potential operator Iα in the weighted Lebesgue generalized spaces Lp(·)(Rn,ρ) with the variable exponent p(x) and a two-parametrical power weight fixed to an arbitrary finite point and to infinity, as well as similar theorems for a spherical analogue of the Riesz potential operator in the corresponding weighted spaces Lp(·)(Sn,ρ) on the unit sphere Sn in Rn+1.  2005 Elsevier Inc. All rights reserved.