Embeddings of Besov–Morrey spaces on bounded domains

2013 ◽  
Vol 218 (2) ◽  
pp. 119-144 ◽  
Author(s):  
Dorothee D. Haroske ◽  
Leszek Skrzypczak
Keyword(s):  
Morrey Spaces ◽  
Bounded Domains

scholarly journals Complex Interpolation of Lizorkin-Triebel-Morrey Spaces on Domains

2020 ◽  
Vol 8 (1) ◽  
pp. 268-304
Author(s):  
Ciqiang Zhuo ◽  
Marc Hovemann ◽  
Winfried Sickel
Keyword(s):  
Morrey Spaces ◽  
Complex Interpolation ◽  
Bounded Domains

AbstractIn this article the authors study complex interpolation of Sobolev-Morrey spaces and their generalizations, Lizorkin-Triebel-Morrey spaces. Both scales are considered on bounded domains. Under certain conditions on the parameters the outcome belongs to the scale of the so-called diamond spaces.

scholarly journals Weighted Hardy Operators in Complementary Morrey Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Dag Lukkassen ◽  
Lars-Erik Persson ◽  
Stefan Samko
Keyword(s):  
Morrey Spaces ◽  
Bounded Domains ◽  
Weighted Lebesgue Space ◽  
Power Functions ◽  
Logarithmic Factor ◽  
Hardy Type ◽  
Weighted Hardy Operators ◽  
Increasing Function ◽  
Hardy Operators ◽  
Hardy Type Operators

We study the weightedp→q-boundedness of the multidimensional weighted Hardy-type operatorsHwαandℋwαwith radial type weightw=w(|x|), in the generalized complementary Morrey spacesℒ∁{0}p,ψ(ℝn)defined by an almost increasing functionψ=ψ(r). We prove a theorem which provides conditions, in terms of some integral inequalities imposed onψandw, for such a boundedness. These conditions are sufficient in the general case, but we prove that they are also necessary when the functionψand the weightware power functions. We also prove that the spacesℒ∁{0}p,ψ(Ω)over bounded domains Ω are embedded between weighted Lebesgue spaceLpwith the weightψand such a space with the weightψ, perturbed by a logarithmic factor. Both the embeddings are sharp.

The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

2020 ◽  
Vol 57 (1) ◽  
pp. 68-90 ◽  
Author(s):  
Tahir S. Gadjiev ◽  
Vagif S. Guliyev ◽  
Konul G. Suleymanova
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Morrey Spaces ◽  
Smooth Bounded Domain ◽  
Weighted Morrey Spaces ◽  
Priori Estimates ◽  
Muckenhoupt Class ◽  
Morrey Estimates ◽  
Dirichlet Boundary Problem

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

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