Boundedness of the maximal, potential and singular operators in the generalized variable exponent Morrey spaces - Guliyev, Vagif S.; Hasanov, Javanshir J.; Samko, Stefan G. (MATHEMATICA SCANDINAVICA, 2010)
We consider generalized Morrey spaces M^p(·),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 R^n 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 M^p(·),ω (Ω)→ M^q(·),ω (Ω)-theorem for the potential operators I^α(·), 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.