Entropy numbers of compact embeddings of smoothness Morrey spaces on bounded domains

Abstract The author first establishes the frame characterizations of Besov and Triebel–Lizorkin spaces on spaces of homogeneous type. As applications, the author then obtains some estimates of entropy numbers for the compact embeddings between Besov spaces or between Triebel–Lizorkin spaces. Moreover, some real interpolation theorems on these spaces are also established by using these frame characterizations and the abstract interpolation method.

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On inclusion properties of discrete Morrey spaces

Georgian Mathematical Journal ◽

10.1515/gmj-2021-2122 ◽

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.

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s-numbers of compact embeddings of function spaces on quasi-bounded domains

Journal of Complexity ◽

10.1016/j.jco.2013.12.003 ◽

2014 ◽

Vol 30 (4) ◽

pp. 495-513 ◽

Cited By ~ 3

Author(s):

Shun Zhang ◽

Alicja Dota

Keyword(s):

Function Spaces ◽

Bounded Domains ◽

Compact Embeddings

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Compact embeddings of radial and subradial subspaces of some Besov-type spaces related to Morrey spaces

Journal of Approximation Theory ◽

10.1016/j.jat.2013.07.001 ◽

2013 ◽

Vol 174 ◽

pp. 121-139 ◽

Cited By ~ 6

Author(s):

Wen Yuan ◽

Winfried Sickel ◽

Dachun Yang

Keyword(s):

Morrey Spaces ◽

Compact Embeddings ◽

Type Spaces ◽

Besov Type Spaces

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Compactness of embeddings of function spaces on quasi-bounded domains and the distribution of eigenvalues of related elliptic operators

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091513000333 ◽

2013 ◽

Vol 56 (3) ◽

pp. 829-851 ◽

Cited By ~ 4

Author(s):

Hans-Gerd Leopold ◽

Leszek Skrzypczak

Keyword(s):

Asymptotic Behaviour ◽

Spectral Properties ◽

Necessary Conditions ◽

Function Spaces ◽

Elliptic Operators ◽

Bounded Domains ◽

Entropy Numbers ◽

Sobolev Embeddings ◽

Distribution Of Eigenvalues ◽

Sufficient And Necessary Conditions

AbstractWe prove sufficient and necessary conditions for compactness of the Sobolev embeddings of Besov and Triebel–Lizorkin spaces defined on bounded and unbounded uniformly E-porous domains. The asymptotic behaviour of the corresponding entropy numbers is calculated. Some applications to the spectral properties of elliptic operators are described.

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Complex Interpolation of Lizorkin-Triebel-Morrey Spaces on Domains

Analysis and Geometry in Metric Spaces ◽

10.1515/agms-2020-0114 ◽

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.

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WITHDRAWN: s-numbers of compact embeddings of function spaces on quasi-bounded domains

Journal of Complexity ◽

10.1016/j.jco.2013.02.002 ◽

2013 ◽

Author(s):

Alicja Gąsiorowska

Keyword(s):

Function Spaces ◽

Bounded Domains ◽

Compact Embeddings

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Embeddings of Besov–Morrey spaces on bounded domains

Studia Mathematica ◽

10.4064/sm218-2-2 ◽

2013 ◽

Vol 218 (2) ◽

pp. 119-144 ◽

Cited By ~ 22

Author(s):

Dorothee D. Haroske ◽

Leszek Skrzypczak

Keyword(s):

Morrey Spaces ◽

Bounded Domains

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Weighted Hardy Operators in Complementary Morrey Spaces

Journal of Function Spaces and Applications ◽

10.1155/2012/283285 ◽

2012 ◽

Vol 2012 ◽

pp. 1-19 ◽

Cited By ~ 1

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.

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