| Singular Measures and Convolution Operators |
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| 作者姓名： | J. M. ALDAZ Juan L. VARONA |
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| 作者单位： | Departamento de Matemdticas y Computación, Universidad de La Rioja, 26004 Logrono, Spain |
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| 基金项目： | Research supported by Grant BFM2003-06335-C03-03 of the DGI |
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| 摘 要： | We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type （1, 1） inequalities. As an application, we prove that the best constants for the centered Hardy-Littlewood maximal operator associated with parallelotopes do not decrease with the dimension.
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| 关 键 词： | 奇异测度 卷积算子 Hardy-Littlewood极大函数 弱型不等式 |
| 收稿时间： | 14 April 2004 |
| 修稿时间： | 2004-04-142004-08-25 |
Singular Measures and Convolution Operators |
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| J. M. ALDAZ Juan L. VARONA.Singular Measures and Convolution Operators[J].Acta Mathematica Sinica,2007,23(3):487-490. |
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| Authors: | J M Aldaz Juan L Varona |
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| Institution: | 1.Departamento de Matemáticas y Computación,Universidad de La Rioja,Logro?o,Spain |
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| Abstract: | We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size
of the constants appearing in weak type (1, 1) inequalities. As an application, we prove that the best constants for the centered
Hardy–Littlewood maximal operator associated with parallelotopes do not decrease with the dimension.
Research supported by Grant BFM2003–06335–C03–03 of the DGI |
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| Keywords: | Hardy-Littlewood maximal function Weak type inequalities Singular measures Convo-lution operators |
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