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Necessary and sufficient conditions for the boundedness of weighted Hardy operators in Hölder spaces
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0003-1963-6829
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Arctic University of Norway, Narvik, Norway.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2018 (English)In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 291, no 11-12, p. 1655-1665Article in journal (Refereed) Published
Abstract [en]

We study one‐ and multi‐dimensional weighted Hardy operators on functions with Hölder‐type behavior. As a main result, we obtain necessary and sufficient conditions on the power weight under which both the left and right hand sided Hardy operators map, roughly speaking, functions with the Hölder behavior only at the singular point to functions differentiable for and bounded after multiplication by a power weight. As a consequence, this implies necessary and sufficient conditions for the boundedness in Hölder spaces due to the corresponding imbeddings. In the multi‐dimensional case we provide, in fact, stronger Hardy inequalities via spherical means. We also separately consider the case of functions with Hölder‐type behavior at infinity (Hölder spaces on the compactified ).

Place, publisher, year, edition, pages
John Wiley & Sons, 2018. Vol. 291, no 11-12, p. 1655-1665
Keywords [en]
boundedness, compactification, Hardy‐type inequalities, Hardy‐type operators, Hölder spaces, spherical means, weighted estimates, Primary: 26D15, 46E15; Secondary: 47B38
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-68198DOI: 10.1002/mana.201700356OAI: oai:DiVA.org:ltu-68198DiVA, id: diva2:1195490
Note

Validerad;2018;Nivå 2;2018-08-09 (andbra)

Available from: 2018-04-05 Created: 2018-04-05 Last updated: 2018-08-09Bibliographically approved

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Burtseva, Evgeniya

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