Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2018; 55(2): 659-672

Online first article January 15, 2018      Printed March 30, 2018

https://doi.org/10.4134/BKMS.b170212

Copyright © The Korean Mathematical Society.

A note of Littlewood-Paley functions on Triebel-Lizorkin spaces

Feng Liu

Shandong University of Science and Technology

Abstract

In this note we prove that several classes of Littlewood-Paley square operators defined by the kernels without any regularity are bounded on Triebel-Lizorkin spaces $F_\alpha^{p,q}(\mathbb{R}^n)$ and Besov spaces $B_\alpha^{p,q}(\mathbb{R}^n)$ for $0<\alpha<1$ and $1

Keywords: Littlewood-Paley function, Triebel-Lizorkin spaces, Besov spaces, extrapolation

MSC numbers: 42B20, 42B25