| LOCAL INEQUALITIES FOR SIDON SUMS AND THEIR APPLICATIONS |
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| 作者姓名： | 范爱华 章逸平 |
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| 作者单位： | [1]DepartmentofMathematics,WuhanUniversity,Wuhan430072,China [2]DepartmentofMathematics,WuhanUniversity,Wuhan430072,China／／LAMFA,CNRSUMR6140.UniversityofPicardie,33RueSaintLeu,80039Amiens,France |
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| 摘 要： | The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sidon series taking values in a Banach space: the summability on a set of positive measure implies the almost everywhere convergence; the contraction principle of Billard-Kahane remains true for Sidon series. As applications, they extend a uniqueness theorem of Zygmund concerning lacunary Fourier series and an analytic continuation theorem of Hadamard concerning lacunary Taylor series. Some of their results still hold for Sidon sets of second kind.
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| 关 键 词： | 西顿集 Khintchine-Kahane不等式 对比原则 独立随机级数 对偶群 局部紧阿贝尔群 |
| 收稿时间： | 10 January 2003 |
LOCAL INEQUALITIES FOR SIDON SUMS AND THEIR APPLICATIONS |
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| Fan Aihua,Zhang Yiping.LOCAL INEQUALITIES FOR SIDON SUMS AND THEIR APPLICATIONS[J].Acta Mathematica Scientia,2005,25(2):305-316. |
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| Authors: | Fan Aihua Zhang Yiping |
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| Institution: | 1. Department of Mathematics, Wuhan University, Wuhan 430072, China;2. LAMFA, CNRS UMR 6140, University of Picardie, 33 Rue Saint Leu, 80039 Amiens, France;3. Department of Mathematics, Wuhan University, Wuhan 430072, China;1. Department of Mathematics, Beijing Normal University, Beijing, 100875, PR China;2. Department of Mathematics, Tianjin Normal University, Tianjin, 300387, PR China;1. Department of Mathematics, The Chinese University of Hong Kong, Hong Kong;2. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China;3. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan |
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| Abstract: | The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sidon series taking values in a Banach space: the summability on a set of positive measure implies the almost everywhere convergence; the contraction principle of Billard-Kahane remains true for Sidon series. As applications, they extend a uniqueness theorem of Zygmund concerning lacunary Fourier series and an analytic continuation theorem of Hadamard concerning lacunary Taylor series. Some of their results still hold for Sidon sets of second kind. |
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| Keywords: | Sidon set Khintchine-Kahane inequality maximal inequality comparison principle contraction principle |
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