文章基本信息

标题：Notes on Transference of Continuity from Maximal Fourier Multiplier Operators on R n to Those on T n
本地全文：下载
作者：Makoto KANEKO ; Enji SATO
期刊名称：Interdisciplinary Information Sciences
印刷版ISSN：1340-9050
电子版ISSN：1347-6157
出版年度：1998
卷号：4
期号：1
页码：97-107
DOI：10.4036/iis.1998.97
出版社：The Editorial Committee of the Interdisciplinary Information Sciences
摘要：Given a sequence { φ _j } of bounded functions on the dual group Γ of a locally compact abelian group G , we have a family of Fourier multiplier operators each element of which is made from a component φ _j of the given sequence. On the other hand, the restrictions φ _j | Λ of φ _j to a subgroup Λ of Γ build Fourier multiplier operators on G ⁄ Λ ^⊥. We are interested in the transference of continuity from the maximal operator constructed by the family of Fourier multiplier operators composed of { φ _j } to the counterpart maximal operator corresponding to { φ _j | Λ }. For the study, it is a powerful tool that, if k ∈ L ¹( Γ ), then the maximal operator corresponding to { k *φ _j } inherits the strong or weak typeness ( p , q ) from the one associated with { φ _j }. First we give a method of showing it. Our result contains the case p = q =1 and our proof is simpler and more straightforward than the one in [2]. Next we consider the case of G = R ⁿ and Λ = Z ⁿ , and develop arguments over Lorentz spaces and Hardy spaces.
关键词：Fourier multiplier;maximal operator;weak type (p,q);Lorentz space;Hardy space