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Stability of approximation under the action of singular integral operators
St. Petersburg Department of the V. A. Steklov Mathematical institute, RAS, Russia.
St. Petersburg Department of the V. A. Steklov Mathematical institute, RAS, Russia.
2006 (English)In: Functional analysis and its applications, ISSN 0016-2663, E-ISSN 1573-8485, Vol. 40, no 4, p. 285-297Article in journal (Refereed) Published
Abstract [en]

Let T be a singular integral operator, and let 0 < α < 1. If t > 0 and the functions f and Tf are both integrable, then there exists a function g ε BLipα(ct)) such that ∥f - g∥≤ Cdist L1 (f, BLipα (t)and ∥Tf-Tg ∥ L 1 ≤ c ∥ f-g ∥ L1 +dist L1 (Tf B Lip α(t)). (Here B X (τ) is the ball of radius τ and centered at zero in the space X; the constants C and c do not depend on t and f.) The function g is independent of T and is constructed starting with f by a nearly algorithmic procedure resembling the classical Calderón-Zygmund decomposition.

Place, publisher, year, edition, pages
2006. Vol. 40, no 4, p. 285-297
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-4162DOI: 10.1007/s10688-006-0045-9ISI: 000243542200004Scopus ID: 2-s2.0-33846163760Local ID: 20e384e0-62b0-11dc-ac97-000ea68e967bOAI: oai:DiVA.org:ltu-4162DiVA, id: diva2:977026
Note

Validerad; 2006; 20070914 (pirkko)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Kruglyak, Natan

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