CONTINUOUS CHARACTERIZATION OF THE TRIEBEL-LIZORKIN SPACES AND FOURIER MULTIPLIERS

Title & Authors
CONTINUOUS CHARACTERIZATION OF THE TRIEBEL-LIZORKIN SPACES AND FOURIER MULTIPLIERS
Cho, Yong-Kum;

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$\small{\ddot{o}}$rmander`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;
Language
English
Cited by
1.
Fourier Multipliers on Triebel-Lizorkin-Type Spaces, Journal of Function Spaces and Applications, 2012, 2012, 1
2.
Musielak–Orlicz Besov-type and Triebel–Lizorkin-type spaces, Revista Matemática Complutense, 2014, 27, 1, 93
3.
Equivalent Quasi-Norms of Besov–Triebel–Lizorkin-Type Spaces via Derivatives, Results in Mathematics, 2017, 72, 1-2, 813
4.
Function spaces of Besov-type and Triebel-Lizorkin-type — a survey, Applied Mathematics-A Journal of Chinese Universities, 2013, 28, 4, 405
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