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The limiting case of the Marcinkiewicz integral: growth for convex sets
Luleå tekniska universitet, Sweden.
Luleå tekniska universitet, Sweden.
2007 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 135, no 10, 3283-3293 p.Article in journal (Refereed) Published
Abstract [en]

The Marcinkiewicz integral Iλ (x)= ∫ (dist (y, ℝn\Ω))λ/Ω| x - y | n+λ dy, where λ > 0, plays a well-known and prominent role in harmonic analysis. In this paper, we estimate the growth of it in the limiting case λ → 0. Throughout, we assume that Ω is convex; it is interesting that this condition cannot be dropped

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2007. Vol. 135, no 10, 3283-3293 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-90401DOI: 10.1090/S0002-9939-07-08856-9OAI: oai:DiVA.org:liu-90401DiVA: diva2:612936
Available from: 2013-03-25 Created: 2013-03-25 Last updated: 2017-12-06

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Kruglyak, Natan

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