Weighted Paley-Wiener theorem on the Hilbert transform
type: Item
instance of: scholarly article
title: Weighted Paley-Wiener theorem on the Hilbert transform
zbMATH Open document ID: 1210.42019
author: Elijah Liflyand
author: Sergey Tikhonov
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2011-01-12T00:00:00Z
review text: The aim of this paper is to prove the weighted analogues of the Paley-Wiener theorem for odd and even functions. In particular, it is shown that for a weight \(w(x)=|x|^\alpha\), the Hilbert transform is bounded in \(L(w)\), when \(-1<\alpha< 1\) provided that \(g\) is odd and monotone on \(\mathbb{R}_+\) or, when \(-2<\alpha< 0\) provided that \(g\) is even and monotone on \(\mathbb{R}_+\). Thus assuming monotonicity or general monotonicity of \(g\) allows to extend Flett's and Hardy-Littlewood results for \(p= 1\).
reviewed by: Som Prakash Goyal
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 5835311
zbMATH Keywords: weighted Paley-Wiener theorem
zbMATH Keywords: Hilbert transform
zbMATH Keywords: even/odd function
MaRDI profile type: Publication
full work available at URL: j.crma.2010.10.028
OpenAlex ID: W2054074360
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DOI: 10.1016/J.CRMA.2010.10.028
description: scientific article; zbMATH DE number 5835311