A few remarks about the Hilbert transform

J. F. Toland

doi:10.1006/jfan.1996.3017

A few remarks about the Hilbert transform

J. F. Toland

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

6 Citations (SciVal)

Abstract

A generalized integral similar to integrability B is used to study the Hilbert transform onX=∑_1≤p<∞L_p(R), with a view to obtaining (i) a mollifier which commutes with the Hilbert transform onXand coincides with the Friedrichs mollifier onL^loc₁(R); (ii) estimates for nonlinear equations; (iii) an integral representation for the Hilbert transform of a regular Schwartz distribution; (iv) a generalized multiplier representation of the Hilbert transform onL₁(R); (v) an elementary proof of the injectivity of H onX.

Original language	English
Pages (from-to)	151-174
Number of pages	24
Journal	Journal of Functional Analysis
Volume	145
Issue number	1
DOIs	https://doi.org/10.1006/jfan.1996.3017
Publication status	Published - 1 Apr 1997

ASJC Scopus subject areas

Analysis

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10.1006/jfan.1996.3017

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AB - A generalized integral similar to integrability B is used to study the Hilbert transform onX=∑1≤p<∞Lp(R), with a view to obtaining (i) a mollifier which commutes with the Hilbert transform onXand coincides with the Friedrichs mollifier onLloc1(R); (ii) estimates for nonlinear equations; (iii) an integral representation for the Hilbert transform of a regular Schwartz distribution; (iv) a generalized multiplier representation of the Hilbert transform onL1(R); (v) an elementary proof of the injectivity of H onX.

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A few remarks about the Hilbert transform

Abstract

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