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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832561103659335680 |
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| author | Natasha Samko |
| author_facet | Natasha Samko |
| author_sort | Natasha Samko |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-949c8c58887e4638af4c706171009f48 |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-949c8c58887e4638af4c706171009f482025-02-03T01:25:58ZengWileyJournal of Function Spaces and Applications0972-68022009-01-0171618910.1155/2009/929041Parameter depending almost monotonic functions and their applications to dimensions in metric measure spacesNatasha Samko0Universidade do Algarve, Campus de Gambelas, Faro 8005-139, PortugalIn 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.http://dx.doi.org/10.1155/2009/929041 |
| spellingShingle | Natasha Samko Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces Journal of Function Spaces and Applications |
| title | Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces |
| title_full | Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces |
| title_fullStr | Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces |
| title_full_unstemmed | Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces |
| title_short | Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces |
| title_sort | parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces |
| url | http://dx.doi.org/10.1155/2009/929041 |
| work_keys_str_mv | AT natashasamko parameterdependingalmostmonotonicfunctionsandtheirapplicationstodimensionsinmetricmeasurespaces |