Journal of Function Spaces

Journal of Function Spaces / 2009 / Article

Open Access

Volume 7 |Article ID 929041 | https://doi.org/10.1155/2009/929041

Natasha Samko, "Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces", Journal of Function Spaces, vol. 7, Article ID 929041, 29 pages, 2009. https://doi.org/10.1155/2009/929041

Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces

Academic Editor: Vladimir D. Stepanov
Received01 Dec 2007

Abstract

In connection with application to various problems of operator theory, we study almost monotonic functions w(x, r) depending on a parameter x which runs a metric measure space X, and the so called index numbers m(w, x), M(w, x) of such functions, and consider some generalized Zygmund, Bary, Lozinskii and Stechkin conditions. The main results contain necessary and sufficient conditions, in terms of lower and upper bounds of indices m(w, x) and M(w, x) , for the uniform belongness of functions w(·, r) to Zygmund-Bary-Stechkin classes. We give also applications to local dimensions in metric measure spaces and characterization of some integral inequalities involving radial weights and measures of balls in such spaces.

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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