Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators |
| |
Authors: | S Samko B Vakulov |
| |
Institution: | a University of Algarve, Portugal b Rostov State University, Russia |
| |
Abstract: | 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. |
| |
Keywords: | Weighted Lebesgue spaces Variable exponent Riesz potentials Spherical potentials Stereographical projection |
本文献已被 ScienceDirect 等数据库收录! |