Hardy operator with variable limits on monotone functions
We characterize weighted Lp-Lq inequalities with the Hardy operator of the form Hf(x)=∫a(x)b(x)f(y)u(y) dy with a non-negative weight function u, restricted to the cone of monotone functions on the semiaxis. The proof is based on the Sawyer criterion and the boundedness of generalized Hardy operator...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2003/860547 |
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| _version_ | 1849397076690993152 |
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| author | Vladimir D. Stepanov Elena P. Ushakova |
| author_facet | Vladimir D. Stepanov Elena P. Ushakova |
| author_sort | Vladimir D. Stepanov |
| collection | DOAJ |
| description | We characterize weighted Lp-Lq inequalities with the Hardy operator of the form Hf(x)=∫a(x)b(x)f(y)u(y) dy with a non-negative weight function u, restricted to the cone of monotone functions on the semiaxis. The proof is based on the Sawyer criterion and the boundedness of generalized Hardy operator with variable limits. |
| format | Article |
| id | doaj-art-a821a05cde624bb98f2c709870a86bcb |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-a821a05cde624bb98f2c709870a86bcb2025-08-20T03:39:09ZengWileyJournal of Function Spaces and Applications0972-68022003-01-011111510.1155/2003/860547Hardy operator with variable limits on monotone functionsVladimir D. Stepanov0Elena P. Ushakova1Department of Mathematics, KAIST, 373-1 Kusong-Dong, Yusong-Gu, Taejon, 305-701, Republic of KoreaComputing Centre FEB RAS, Tikhookeanskaya 153, Khabarovsk, 680042, RussiaWe characterize weighted Lp-Lq inequalities with the Hardy operator of the form Hf(x)=∫a(x)b(x)f(y)u(y) dy with a non-negative weight function u, restricted to the cone of monotone functions on the semiaxis. The proof is based on the Sawyer criterion and the boundedness of generalized Hardy operator with variable limits.http://dx.doi.org/10.1155/2003/860547 |
| spellingShingle | Vladimir D. Stepanov Elena P. Ushakova Hardy operator with variable limits on monotone functions Journal of Function Spaces and Applications |
| title | Hardy operator with variable limits on monotone functions |
| title_full | Hardy operator with variable limits on monotone functions |
| title_fullStr | Hardy operator with variable limits on monotone functions |
| title_full_unstemmed | Hardy operator with variable limits on monotone functions |
| title_short | Hardy operator with variable limits on monotone functions |
| title_sort | hardy operator with variable limits on monotone functions |
| url | http://dx.doi.org/10.1155/2003/860547 |
| work_keys_str_mv | AT vladimirdstepanov hardyoperatorwithvariablelimitsonmonotonefunctions AT elenapushakova hardyoperatorwithvariablelimitsonmonotonefunctions |