Resumen de Boundedness of the maximal, potential and singular operators in the generalized variable exponent Morrey spaces

Vagif S. Guliyev, Javanshir J. Hasanov, Stefan Samko

• We consider generalized Morrey spaces Mp(⋅),ω(Ω) with variable exponent p(x) and a general function ω(x,r) defining the Morrey-type norm. In case of bounded sets Ω⊂Rn we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove a Sobolev-Adams type Mp(⋅),ω(Ω)→Mq(⋅),ω(Ω)-theorem for the potential operators Iα(⋅), also of variable order. The conditions for the boundedness are given it terms of Zygmund-type integral inequalities on ω(x,r), which do not assume any assumption on monotonicity of ω(x,r) in r.