Research article

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

  • Received: 26 March 2016 Accepted: 11 April 2016 Published: 19 April 2016
  • In this paper, we are devoted to establishing several necessary and sufficient conditions for $f\in L^{p}(\mathbb{R}^{n}),\ g\in L^{q}(\mathbb{R}^{n})$ with $\frac{1}{p}+\frac{1}{q}\leq 1$ to satisfy the Bedrosian identity $H(fg)=fHg$, where $H$ denotes the n-dimensional Hilbert transform. In addition, we also show that the distribution $f\in \mathcal{D}'_{L^{p}}(\mathbb{R}^{n})$ can be represented by functions in the Hardy space on tube.

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

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  • In this paper, we are devoted to establishing several necessary and sufficient conditions for $f\in L^{p}(\mathbb{R}^{n}),\ g\in L^{q}(\mathbb{R}^{n})$ with $\frac{1}{p}+\frac{1}{q}\leq 1$ to satisfy the Bedrosian identity $H(fg)=fHg$, where $H$ denotes the n-dimensional Hilbert transform. In addition, we also show that the distribution $f\in \mathcal{D}'_{L^{p}}(\mathbb{R}^{n})$ can be represented by functions in the Hardy space on tube.
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    © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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