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Title: Alternative characterisations of Lorentz-Karamata spaces (English)
Author: Edmunds, D. E.
Author: Opic, B.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 58
Issue: 2
Year: 2008
Pages: 517-540
Summary lang: English
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Category: math
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Summary: We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces. (English)
Keyword: Lorentz-Karamata spaces
Keyword: equivalent quasi-norms
Keyword: weighted norm inequalities
Keyword: fractional maximal operators
Keyword: Riesz potentials
MSC: 26D10
MSC: 42B35
MSC: 46E30
MSC: 47B38
MSC: 47G10
idZBL: Zbl 1174.46019
idMR: MR2411107
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Date available: 2009-09-24T11:56:43Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/128275
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