Weighted Hardy Operators in Complementary Morrey Spaces
Joint Authors
Lukkassen, Dag
Samko, Stefan
Persson, Lars-Erik
Source
Journal of Function Spaces and Applications
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-01-08
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
We study the weighted p→q-boundedness of the multidimensional weighted Hardy-type operators Hwα and ℋwα with radial type weight w=w(|x|), in the generalized complementary Morrey spaces ℒ∁{0}p,ψ(ℝn) defined by an almost increasing function ψ=ψ(r).
We prove a theorem which provides conditions, in terms of some integral inequalities imposed on ψ and w, for such a boundedness.
These conditions are sufficient in the general case, but we prove that they are also necessary when the function ψ and the weight w are power functions.
We also prove that the spaces ℒ∁{0}p,ψ(Ω) over bounded domains Ω are embedded between weighted Lebesgue space Lp with the weight ψ and such a space with the weight ψ, perturbed by a logarithmic factor.
Both the embeddings are sharp.
American Psychological Association (APA)
Lukkassen, Dag& Persson, Lars-Erik& Samko, Stefan. 2013. Weighted Hardy Operators in Complementary Morrey Spaces. Journal of Function Spaces and Applications،Vol. 2012, no. 2012, pp.1-19.
https://search.emarefa.net/detail/BIM-460177
Modern Language Association (MLA)
Lukkassen, Dag…[et al.]. Weighted Hardy Operators in Complementary Morrey Spaces. Journal of Function Spaces and Applications No. 2012 (2012), pp.1-19.
https://search.emarefa.net/detail/BIM-460177
American Medical Association (AMA)
Lukkassen, Dag& Persson, Lars-Erik& Samko, Stefan. Weighted Hardy Operators in Complementary Morrey Spaces. Journal of Function Spaces and Applications. 2013. Vol. 2012, no. 2012, pp.1-19.
https://search.emarefa.net/detail/BIM-460177
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-460177