(1) Departamento de Matemática, Universidade de Aveiro, 3810-193 Aveiro, Portugal;(2) Faculdade de Ciências e Tecnologia, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal
Abstract:
We prove the continuity of potential type operators and hypersingular operators in variable Lebesgue and Sobolev spaces on a metric measure space (Χ, d, μ). Two variants of such operators are considered, according to the regularity admitted on the measure μ.