scholarly journals Some quantitative result on compact embeddings in smoothness Morrey spaces on bounded domains; an approach via interpolation

2019 ◽  
Vol 119 ◽  
pp. 181-191
Author(s):  
Dorothee D. Haroske ◽  
Leszek Skrzypczak
Keyword(s):  
Quantitative Result ◽  
Morrey Spaces ◽  
Bounded Domains ◽  
Compact Embeddings

On inclusion properties of discrete Morrey spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hendra Gunawan ◽  
Denny Ivanal Hakim ◽  
Mochammad Idris
Keyword(s):  
Weak Type ◽  
Morrey Spaces ◽  
Sequence Spaces ◽  
Necessary Condition ◽  
Inclusion Properties ◽  
Compact Embeddings ◽  
Inclusion Relations ◽  
Pitt’S Theorem

Abstract We discuss a necessary condition for inclusion relations of weak type discrete Morrey spaces which can be seen as an extension of the results in [H. Gunawan, E. Kikianty and C. Schwanke, Discrete Morrey spaces and their inclusion properties, Math. Nachr. 291 2018, 8–9, 1283–1296] and [D. D. Haroske and L. Skrzypczak, Morrey sequence spaces: Pitt’s theorem and compact embeddings, Constr. Approx. 51 2020, 3, 505–535]. We also prove a proper inclusion from weak type discrete Morrey spaces into discrete Morrey spaces. In addition, we give a necessary condition for this inclusion. Some connections between the inclusion properties of discrete Morrey spaces and those of Morrey spaces are also discussed.

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.

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 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.

Sign in / Sign up

Export Citation Format

Share Document