| On a Measure of Non-compactness for Some Classical Operators |
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| 引用本文： | David E. EDMUNDS Alberto FIORENZA Alexander MESKHI. On a Measure of Non-compactness for Some Classical Operators[J]. 数学学报(英文版), 2006, 22(6): 1847-1862. DOI: 10.1007/s10114-005-0674-6 |
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| 作者姓名： | David E. EDMUNDS Alberto FIORENZA Alexander MESKHI |
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| 作者单位： | [1]School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4 YH, United Kingdom [2]Dipartimento di Costruzioni e Metodi Matematici in Architettura, Universita＇ di Napoli Federico IL via Monteoliveto, 3, 80134 - Napoli （NA） Italy [3]Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy |
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| 基金项目： | Acknowledgements The third author expresses his gratitude to the School of Mathematics of Cardiff University and, in particular, to Prof. W. D. Evans for support during a visit to the University of Sussex. The third author is also grateful to G.N.A.M.P.A. for support during the visit to the Universita di Napoli ＂Federico II＂. The authors thank Prof. V. Kokilashvili for his valuable suggestions and remarks. |
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| 摘 要： |
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| 关 键 词： | 非紧密测量 最大函数 奇异积分 Hilbert变换 |
| 收稿时间： | 2005-07-21 |
| 修稿时间： | 2005-07-212005-12-22 |
On a Measure of Non–compactness for Some Classical Operators |
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| David E. Edmunds,Alberto Fiorenza,Alexander Meskhi. On a Measure of Non–compactness for Some Classical Operators[J]. Acta Mathematica Sinica(English Series), 2006, 22(6): 1847-1862. DOI: 10.1007/s10114-005-0674-6 |
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| Authors: | David E. Edmunds Alberto Fiorenza Alexander Meskhi |
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| Affiliation: | (1) School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4YH, United Kingdom;(2) Dipartimento di Costruzioni e Metodi Matematici in Architettura, Universita’ di Napoli Federico II, via Monteoliveto, 3, 80134 Napoli (NA), Italy;(3) Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy |
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| Abstract: | The measure of non-compactness is estimated from below for various operators, including the Hardy-Littlewood maximal operator, the fractional maximal operator and the Hilbert transform, all acting between weighted Lebesgue spaces. The identity operator acting between weighted Lebesgue spaces and also between the counterparts of these spaces with variable exponents is similarly analysed. These results enable the lack of compactness of such operators to be quantified. |
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| Keywords: | measure of non-compactness maximal functions singular integrals embeddings weight |
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