NON-SMOOTH DECOMPOSITION AND
THE MARCINKIEWICZ INTEGRAL
Keisuke Asami
Department of Mathematics and Information Sciences
Tokyo Metropolitan University
1-1 Minamiosawa, Hachioji
Tokyo 192-0397, JAPAN

Abstract

We develop a theory of non-smooth decomposition in homogeneous Triebel-Lizorkin spaces. As a byproduct, we can recover the decomposition results for Hardy spaces as a special case. The result extends what Frazier and Jawerth obtained in 1990. The result by Frazier and Jawerth covers only the limited range of the parameters but the result in this paper is valid for all admissible parameters for Triebel-Lizorkin spaces. As an application of the main results, we prove that the Marcinkiewicz operator is bounded. What is new in this paper is to reconstruct sequence spaces other than classical $\ell^p$ spaces.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 30
Issue: 6
Year: 2017

DOI: 10.12732/ijam.v30i6.7

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