On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces

Boundedness of the Maximal, Potential and Singular Operators in the Generalized Morrey Spaces

We consider generalized Morrey spaces Mp,ω R with a general function ω x, r defining the Morrey-type norm. We find the conditions on the pair ω1, ω2 which ensures the boundedness of the maximal operator and Calderón-Zygmund singular integral operators from one generalized Morrey space Mp,ω1 R to another Mp,ω2 R , 1 < p < ∞, and from the space M1,ω1 R to the weak space WM1,ω2 R . We also prove a...

Boundedness of Multilinear Integral Operators and Their Commutators on Generalized Morrey Spaces

Generalized Fractional Integral Operators on Vanishing Generalized Local Morrey Spaces

In this paper, we prove the Spanne-Guliyev type boundedness of the generalized fractional integral operator Iρ from the vanishing generalized local Morrey spaces V LM {x0} p,φ1 to V LM {x0} q,φ2 , 1 < p < q < ∞, and from the space V LM {x0} 1,φ1 to the weak space VWLM {x0} q,φ2 , 1 < q < ∞. We also prove the Adams-Guliyev type boundedness of the operator Iρ from the vanishing generalized Morrey...

Boundedness of the Fractional Maximal Operator in Local Morrey-type Spaces

The problem of the boundedness of the fractional maximal operator Mα, 0 ≤ α < n in local Morrey-type spaces is reduced to the problem of the boundedness of the Hardy operator in weighted Lp-spaces on the cone of non-negative non-increasing functions. This allows obtaining sharp sufficient conditions for the boundedness for all admissible values of the parameters.

Boundedness of Singular Integral Operators On

Eleonor Harboure Beairiz Viviani Presentado pOl" Carlos Segovia Abstract: We study the boundedness of singular integral operators on Orlicz-Hardy spaces H w , in the setting of spaces of homogeneous type. As an application of this result, we obtain a characterization of HwIRn in terms of the Riesz Transforms. § 1. NOTATION AND DEFINITIONS Let X be a set. A function d : X x X -+ IR+ U {OJ shall ...