Hilbert transforms and Lagrange interpolation
type: Item
instance of: scholarly article
title: Hilbert transforms and Lagrange interpolation
zbMATH Open document ID: 0701.41003
DOI: 10.1016/0021-9045(90)90065-X
published in: Journal of Approximation Theory
publication date: 1990-01-01T00:00:00Z
review text: This note completes the author's paper ``Mean convergence of Lagrange Interpolation III'' [Trans. Am. Math. Soc. 282, 669-698 (1984; Zbl 0577.41001)] where the formula \(\int_{{\mathbb{R}}}H(F)G=- \int_{{\mathbb{R}}}H(G)F\) (H is the Hilbert transform) is used. It is known that this formula is true for \(F\in L_ p\) and \(G\in L_ q\), \(1<p\), \(q<\infty\), \(1/p+1/q=1\). The author shows that for F and G having compact supports, \(F\in L \log^+L\) and \(G\in L_{\infty}\), the formula holds as well. The proof of this statement is due to Harold Widom.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 4148802
zbMATH Keywords: H\({}_ p\)-spaces
author: Paul Nevai
reviewed by: Radu Precup
MaRDI profile type: Publication
cites work: Q5336643
cites work: Q3922907
cites work: Q3731971
cites work: Mean Convergence of Lagrange Interpolation. III
cites work: Q5607484
cites work: Q5769133
cites work: Q4143689
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description: scientific article; zbMATH DE number 4148802