Multipliers from \(H^1\) to \(L^p\)
type: Item
instance of: scholarly article
title: Multipliers from \(H^1\) to \(L^p\)
zbMATH Open document ID: 1031.42007
DOI: 10.1007/BF02384776
author: Andreas Nilsson
published in: Arkiv för Matematik
publication date: 2003-09-30T00:00:00Z
review text: The author proves a theorem which combines the Hörmander-Mikhlin multiplier theorem for Hardy spaces in [\textit{L. Hörmander}, Acta Math. 104, 93-140 (1960; Zbl 0093.11402)] with a result of \textit{R. Johnson} in [Ark. Mat. 16, 235-249 (1978; Zbl 0402.46024)]. Let \(\Delta_j=\{2^{j-1}\leq|\xi|\leq 2^{j+1}\}\). Assume that \(m\in C^k(\mathbb{R}^n\setminus\{0\})\) and that \[ \int_{\Delta_j}\sum_{|\alpha|\leq k} \left|2^{j|\alpha|}D_\alpha m(\xi)\right|^2 d\xi\leq 2^{nj(2-q)/q}, \quad j\in \mathbb{Z}, \] where \(k\) is the least integer \(>n(2-q)/2q\) and \(1\leq q\leq 2\). Then the author proves that the convolution operator defined by \(K=\widehat m\) continuously maps \(H^1(\mathbb{R}^n)\) to \(L^q(\mathbb{R}^n)\).
Mathematics Subject Classification ID: 42B15
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 42B30
zbMATH DE Number: 1987637
zbMATH Keywords: Hörmander-Mikhlin multiplier
zbMATH Keywords: Hardy spaces
reviewed by: Dachun Yang
MaRDI profile type: Publication
cites work: Fourier multipliers from \(H^1(R^n)\) to \(L^P(R^N)\)
cites work: \(H^p\) spaces of several variables
cites work: Estimates for translation invariant operators in \(L^p\) spaces
cites work: Multipliers of \(H^p\) spaces
full work available at URL: https://doi.org/10.1007/bf02384776
OpenAlex ID: W2998406531
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description: scientific article; zbMATH DE number 1987637