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Bull. Korean Math. Soc. 2010; 47(4): 839-857

Printed July 1, 2010

https://doi.org/10.4134/BKMS.2010.47.4.839

Copyright © The Korean Mathematical Society.

Continuous Characterization of the Triebel-Lizorkin Spaces and Fourier Multipliers

Yong-Kum Cho

Chung-Ang University

Abstract

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We give a set of continuous characterizations for the homogeneous Triebel-Lizorkin spaces and use them to study boundedness properties of Fourier multiplier operators whose symbols satisfy a generalization of H\"ormander's condition. As an application, we give new direct proofs of the imbedding theorems of the Sobolev type.

Keywords: Fourier multiplier, Sobolev imbedding, Triebel-Lizorkin spaces, Besov-Lipschitz spaces, singular integrals

MSC numbers: Primary 42B15, 42B35, 46E35

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