Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces
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, Lozinski...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/929041 |
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| Summary: | 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. |
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| ISSN: | 0972-6802 |