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A Few Remarks about the Hilbert Transform

✍ Scribed by J.F. Toland

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
393 KB
Volume
145
Category
Article
ISSN
0022-1236

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✦ Synopsis

A generalized integral similar to integrability B is used to study the Hilbert transform on X= 1 p< L p (R), with a view to obtaining (i) a mollifier which commutes with the Hilbert transform on X and coincides with the Friedrichs mollifier on L loc 1 (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 on L 1 (R); (v) an elementary proof of the injectivity of H on X.

1997 Academic Press

In a recent study of nonlinear equations involving the Hilbert transform [22] it was useful to know that if u # 1 p< L p (R) (this notation article no. FU963017

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