The Bedrosian Identity for Lp Function and the Hardy Space on Tube

AIMS Mathematics

关键词: : ;    Bedrosian identity;    Fourier transform;    Hilbert transform;    Distribution;   

DOI  :  10.3934/Math.2016.1.9

学科分类：数学（综合）

来源: AIMS Press

【 摘 要 】

In this paper, we are devoted to establishing several necessary and su cient conditions for f∈L^p(Rⁿ); g∈L^q(Rⁿ) with (1/p) +(1/q)≤1 to satisfy the Bedrosian identity H(fg) =fHg, where H denotes the n-dimensional Hilbert transform. In addition, we also show that the distribution f∈DL^p' (Rⁿ) can be represented by functions in the Hardy space on tube.

【 授权许可】

CC BY