LOCAL INEQUALITIES FOR SIDON SUMS AND THEIR APPLICATIONS  

作　　者：范爱华 章逸平 

机构地区：[1]Department of Mathematics Wuhan University,Wuhan 430072,China,LAMFA,CNRS UMR 6140,University of Picardie,33 Rue Saint Leu,80039 Amiens,France [2]Department of Mathematics Wuhan University,Wuhan 430072,China

出　　处：《Acta Mathematica Scientia》2005年第2期305-316,共12页数学物理学报（B辑英文版）

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.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.

关 键 词：Sidon set. Khintchine-Kahanc inequality maximal inequality comparison principle contraction principle 

分 类 号：O178[理学—数学]