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Weighted Hardy-type inequalities in variable exponent Morrey-type spaces
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- Lukkassen, Dag (author)
- Narvik University College and Norut Narvik
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- Persson, Lars-Erik (author)
- Luleå tekniska universitet,Matematiska vetenskaper
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- Samko, Stefan (author)
- Universidade do Algarve, FCT, Campus de Gambelas
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- Hindawi Limited, 2013
- 2013
- English.
- In: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965.
- Journal article (peer-reviewed)
Abstract
Subject headings
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- We study the p(.) -> q(.) boundedness of weighted multidimensional Hardy-type operators H-w(alpha(.)) and H-w(alpha(.)) of variable order alpha(x), with radial weight w(vertical bar x vertical bar), from a variable exponent locally generalized Morrey space L-p(.),L-phi(.)(R-n, w) to another L-q(.),L-psi(.)(R-n, w). The exponents are assumed to satisfy the decay condition at the origin and infinity. We construct certain functions, defined by p, alpha, and phi, the belongness of which to the resulting space L-q(.),L-psi(.)(R-n, w) is sufficient for such a boundedness. Under additional assumptions on phi/w, this condition is also necessary. We also give the boundedness conditions in terms of Zygmund-type integral inequalities for the functions phi and phi/w.
Subject headings
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- Matematik
- Mathematics
Publication and Content Type
- ref (subject category)
- art (subject category)
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- Wall, Peter
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- NATURAL SCIENCES
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- Luleå University of Technology
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