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Spring and Summer 2017 The Hörmander multiplier theorem, I: The linear case revisited
Loukas Grafakos, Danqing He, Petr Honzik, Hanh Van Nguyen
Illinois J. Math. 61(1-2): 25-35 (Spring and Summer 2017). DOI: 10.1215/ijm/1520046207

Abstract

We discuss $L^{p}(\mathbb{R}^{n})$ boundedness for Fourier multiplier operators that satisfy the hypotheses of the Hörmander multiplier theorem in terms of an optimal condition that relates the distance $\vert \frac{1}{p}-\frac{1}{2}\vert $ to the smoothness $s$ of the associated multiplier measured in some Sobolev norm. We provide new counterexamples to justify the optimality of the condition $\vert \frac{1}{p}-\frac{1}{2}\vert <\frac{s}{n}$ and we discuss the endpoint case $\vert \frac{1}{p}-\frac{1}{2}\vert =\frac{s}{n}$.

Citation

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Loukas Grafakos. Danqing He. Petr Honzik. Hanh Van Nguyen. "The Hörmander multiplier theorem, I: The linear case revisited." Illinois J. Math. 61 (1-2) 25 - 35, Spring and Summer 2017. https://doi.org/10.1215/ijm/1520046207

Information

Received: 2 December 2016; Revised: 17 November 2017; Published: Spring and Summer 2017
First available in Project Euclid: 3 March 2018

zbMATH: 1395.42025
MathSciNet: MR3770834
Digital Object Identifier: 10.1215/ijm/1520046207

Subjects:
Primary: 42B15, 42B20, 42B30, 42B99

Rights: Copyright © 2017 University of Illinois at Urbana-Champaign

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Vol.61 • No. 1-2 • Spring and Summer 2017
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