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Inequalities for moduli of continuity and rearrangements
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
1991 (English)In: Conference on Approximation Theory, in Kecskemét, August 6 to 11, 1990 / [ed] Károly Tandory; József Szabados, Elsevier, 1991, 412-423 p.Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we consider measurable functions f from a symmetric space X on [0,1]. We prove some inequalities relating the behavior of the nonincreasing rearrangement f* and the (generalized) modulus of continuity ωX (t,f). In particular, we generalize, complement and unify some previous result by Brudnyi, Garsia and Rodemich, Milman, Osvald, Storozhenko, and Wik. We note that these inequalities have direct applications, e.g. in the theory of imbedding of symmetric spaces and Besov (Lipschitz) spaces, Fourier analysis and the theory of stochastic processes. This paper is organized in the following way: In Section 1 we give some basic definitions and other preliminaries. In Section 2 we present a generalization of the Storozhenko inequality to the case of symmetric spaces thereby sharpening a previous result of Milman. We also include a generalization of the Garsia-Rodemich inequality to these spaces. In Section 3 we present and prove the Brudnyi-Osvald-Wik inequality for the case of symmetric spaces.

Place, publisher, year, edition, pages
Elsevier, 1991. 412-423 p.
Series
Colloquia mathematica Societatis János Bolyai, ISSN 0139-3383 ; 58
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-34305ISI: A1991BY77E00029Local ID: 87912560-7b0d-11dc-a72d-000ea68e967bISBN: 0-444-98695-2 (print)OAI: oai:DiVA.org:ltu-34305DiVA: diva2:1007555
Conference
Approximation theory : 06/08/1990 - 11/08/1990
Note

Godkänd; 1991; 20071015 (evan)

Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2017-11-25Bibliographically approved

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