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Smooth and nonsmooth Calderón-Zygmund type decompositions for Morrey spaces
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
2005 (English)In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 11, no 6, p. 697-714Article in journal (Refereed) Published
Abstract [en]

It is shown that it is possible to construct an analogue of the Calderón-Zygmund decomposition for the Morrey spaces Morλ for the entire interval λ ∈ (0,1]. Moreover, for λ ∈ (1-,1] it is possible to construct a smooth analogue of the Calderón-Zygmund decomposition. The reason why we do not have any smooth analogues for the entire interval λ ∈ (0,1] is related to the following interesting property of cubes in the Whitney decomposition lemma: The sum of the volumes of Whitney cubes to the power λ is equal to infinity for λ ∈ (0,1-(1/n)].

Place, publisher, year, edition, pages
2005. Vol. 11, no 6, p. 697-714
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-2954DOI: 10.1007/s00041-005-5032-7ISI: 000234544400006Scopus ID: 2-s2.0-29644447518Local ID: 0b313580-a52c-11db-8975-000ea68e967bOAI: oai:DiVA.org:ltu-2954DiVA, id: diva2:975809
Note
Validerad; 2005; 20070116 (evan)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Kruglyak, NatanKuznetsov, Evgeny

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