On the measure of non-compactness of maximal operators
In one of the previous articles of the author it was proved that if B is a convex quasi-density measurable basis and E is a symmetric space on Rn with respect to the Lebesgue measure, then there do not exist non-orthogonal weights w and v for which the maximal operator MB corresponding to B acts com...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2004/786419 |
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| _version_ | 1850165676274089984 |
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| author | Georgi G. Oniani |
| author_facet | Georgi G. Oniani |
| author_sort | Georgi G. Oniani |
| collection | DOAJ |
| description | In one of the previous articles of the author it was proved that if B is a convex quasi-density measurable basis and E is a symmetric space on Rn with respect to the Lebesgue measure, then there do not exist non-orthogonal weights w and v for which the maximal operator MB corresponding to B acts compactly from the weight space Ew to the weight space Ev. Here it is given the generalization of this result, in particular, it is estimated from below the measure of non-compactness of the mentioned operators. |
| format | Article |
| id | doaj-art-ee8d9e8c5e3a4ffbbbdff05de99690d9 |
| institution | OA Journals |
| issn | 0972-6802 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-ee8d9e8c5e3a4ffbbbdff05de99690d92025-08-20T02:21:41ZengWileyJournal of Function Spaces and Applications0972-68022004-01-012221722510.1155/2004/786419On the measure of non-compactness of maximal operatorsGeorgi G. Oniani0Department of Physics and Mathematics, Kutaisi State University, 55, Tamar Mepe St., Kutaisi 4600, GeorgiaIn one of the previous articles of the author it was proved that if B is a convex quasi-density measurable basis and E is a symmetric space on Rn with respect to the Lebesgue measure, then there do not exist non-orthogonal weights w and v for which the maximal operator MB corresponding to B acts compactly from the weight space Ew to the weight space Ev. Here it is given the generalization of this result, in particular, it is estimated from below the measure of non-compactness of the mentioned operators.http://dx.doi.org/10.1155/2004/786419 |
| spellingShingle | Georgi G. Oniani On the measure of non-compactness of maximal operators Journal of Function Spaces and Applications |
| title | On the measure of non-compactness of maximal operators |
| title_full | On the measure of non-compactness of maximal operators |
| title_fullStr | On the measure of non-compactness of maximal operators |
| title_full_unstemmed | On the measure of non-compactness of maximal operators |
| title_short | On the measure of non-compactness of maximal operators |
| title_sort | on the measure of non compactness of maximal operators |
| url | http://dx.doi.org/10.1155/2004/786419 |
| work_keys_str_mv | AT georgigoniani onthemeasureofnoncompactnessofmaximaloperators |