Inequalities for moduli of continuity and rearrangements

Godkänd; 1991; 20071015 (evan)
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.

Maligranda, Lech (author)
Persson, Lars-ErikLuleå tekniska universitet,Matematiska vetenskaper(Swepub:ltu)larserik (author)
Luleå tekniska universitetMatematiska vetenskaper (creator_code:org_t)

In:Conference on Approximation Theory, in Kecskemét, August 6 to 11, 1990: Elsevier, s. 412-4230444986952

By the author/editor: Johansson, Hans; Maligranda, Lech; Persson, Lars-Er ...

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Mathematical Ana ...

Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.