New 2-Microlocal Besov and Triebel-Lizorkin Spaces via the Littlewood-Paley Decomposition


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Authors

  • Koichi Saka

Keywords:

wavelet, Besov space, Triebel-Lizorkin space, pseudo-differential operator, Calderón-Zygmund operator, atomic and molecular decomposition, 2-microlocal space, φ-transform

Abstract

In this paper we introduce and investigate new 2-microlocal Besov and Triebel-Lizorkin spaces via the Littlewood-Paley decomposition. We establish characterizations of these function spaces by the φ-transform, the atomic and molecular decomposition and the wavelet decomposition. As applications we prove boundedness of the Calderón-Zygmund operators and the pseudo-differential operators on the function spaces. Moreover, we give characterizations via oscillations and differences.

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Published

2023-01-01

How to Cite

Saka, K. (2023). New 2-Microlocal Besov and Triebel-Lizorkin Spaces via the Littlewood-Paley Decomposition. Eurasian Mathematical Journal, 14(3), 75–111. Retrieved from https://emj.enu.kz/index.php/main/article/view/293

Issue

Vol. 14 No. 3 (2023)

Section

Articles