AIMS Mathematics, 2016, 1(1): 9-23. doi: 10.3934/Math.2016.1.9.

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

School of Mathematical Sciences, Key Laboratory of Mathematics and Complex Systems ofMinistry of Education, Beijing Normal University, 100875, Beijing, China

In this paper, we are devoted to establishing several necessary and su cient conditions for fLp(Rn); gLq(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 fDLp' (Rn) can be represented by functions in the Hardy space on tube.
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Keywords Bedrosian identity; Fourier transform; Hilbert transform; Distribution

Citation: Zhihong Wen, Guantie Deng. The Bedrosian Identity for Lp Function and the Hardy Space on Tube. AIMS Mathematics, 2016, 1(1): 9-23. doi: 10.3934/Math.2016.1.9

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