Inequalities for moduli of continuity and rearrangements
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 (Refereed)
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.
, Colloquia mathematica Societatis János Bolyai, ISSN 0139-3383 ; 58
Research subject Mathematics
IdentifiersURN: urn:nbn:se:ltu:diva-34305Local ID: 87912560-7b0d-11dc-a72d-000ea68e967bISBN: 0-444-98695-2ISBN: 9-638022-64-7OAI: oai:DiVA.org:ltu-34305DiVA: diva2:1007555
Approximation theory : 06/08/1990 - 11/08/1990
Godkänd; 1991; 20071015 (evan)2016-09-302016-09-30Bibliographically approved