BOUNDEDNESS OF MAXIMAL, POTENTIAL TYPE,AND SINGULAR INTEGRAL OPERATORS IN THE GENERALIZED VARIABLE EXPONENT MORREY TYPE SPACES

摘要

We consider generalized Morrey type spaces M~(p(·),0(.),ω(·))(Ω) with variable exponents p(x), θ(r) and a general function ω(x,r) defining a Morrey type norm. In the case of bounded sets Ω C R~n, we prove the boundedness of the Hardy Little wood maximal operator and Calderon-Zygrnund singular integral operators with standard kernel. We prove a Sobolev-Adams type embedding theorem M~(p(.),θ_1(·),ω_1(·)) (Ω)→M~(p(·),θ_2(.),ω_2(·)) (Ω) for the potential type operator I~(a(·)) of variable order. In all the cases, we do not impose any monotonicity type conditions on ω(x,r) with respect to r.