Abstract
In this paper, we study the boundedness of the sublinear operators, generated by Calderon–Zygmund operators in local generalized Morrey spaces. By using these results we prove the solvability of the Dirichlet boundary value problem for a polyharmonic equation in modified local generalized Sobolev–Morrey spaces. We obtain a priori estimates for the solutions of the Dirichlet boundary value problems for the uniformly elliptic equations in modified local generalized Sobolev–Morrey spaces defined on bounded smooth domains.
Highlights
The classical Morrey spaces Lp,λ are originally introduced in order to study the local behavior of solutions to elliptic partial differential equations
[31] Mizuhara extended the Morrey’s concept of integral average over a ball with a certain growth, taking a weight function φ(x, r) : Rn × R+ → R+ instead of rλ. He put the beginning of the study of the generalized Morrey spaces Mp,φ, p > 1 with φ belonging to various classes of weight functions
In this paper we study the boundedness of the sublinear operators, generated by Calderón–Zygmund operators in local generalized Morrey spaces
Summary
The classical Morrey spaces Lp,λ are originally introduced in order to study the local behavior of solutions to elliptic partial differential equations. These results allow us to study the regularity of the solutions of various linear elliptic and parabolic boundary value problems in Mp,φ (see [27, 28, 38]) Later these results are extended on the local generalized Morrey spaces, which is obtained the boundedness of the Calderón–Zygmund operators from one local generalized Morrey space LM{p,xφ01}(Rn) to another LM{p,xφ02}(Rn), x0 ∈ Rn (see [25, 26]), if the pair functions (φ1, φ2) satisfy the following condition n supt
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