Estimates near \(L^ 1\) for Fourier multipliers and maximal functions
type: Item
instance of: scholarly article
title: Estimates near \(L^ 1\) for Fourier multipliers and maximal functions
zbMATH Open document ID: 0655.42012
DOI: 10.1007/BF01198570
author: Andreas Seeger
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: The following endpoint estimate of the Hörmander multiplier theorem is proved: Suppose that the bounded function \(m\) belongs to the localized Besov-space defined by the norm \(\|\varphi m(t\cdot)\| _{B^2_{n| 2,1}}\), where \(\varphi\) is a suitable bump-function supported away from 0. Then the operator \(T_ m\), defined by \([T_ mf]^\wedge =mf^\wedge\), is bounded from the Hardy-space \(H^1\) into the Lorentz-space \(L^{12}\). Furthermore, a weak-type-(1-1)-inequality for maximal-functions \(\sup | F^{-1}[m(t\cdot)f^\wedge)| (x)\) is obtained.
Mathematics Subject Classification ID: 42B15
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 4069529
zbMATH Keywords: Hörmander multiplier theorem
zbMATH Keywords: Besov-space
zbMATH Keywords: maximal-functions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01198570
OpenAlex ID: W2001597998
description: scientific article; zbMATH DE number 4069529