Continuous Characterization of the Triebel-Lizorkin Spaces and Fourier Multipliers
Bull. Korean Math. Soc. 2010 Vol. 47, No. 4, 839-857
https://doi.org/10.4134/BKMS.2010.47.4.839
Published online July 1, 2010
Yong-Kum Cho
Chung-Ang University
Abstract : 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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