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Bull. Korean Math. Soc. 2015; 52(3): 851-864

Printed May 31, 2015

https://doi.org/10.4134/BKMS.2015.52.3.851

Copyright © The Korean Mathematical Society.

Pointwise estimates and boundedness of generalized Littlewood-Paley operators in $BMO(\mathbb{R}^n)$

Yurong Wu and Huoxiong Wu

Zhejiang University of Technology, Xiamen University

Abstract

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In this paper, we study the generalized Littlewood-Paley operators. It is shown that the generalized $g$-function, Lusin area function and $g_\lambda^*$-function on any BMO function are either infinite everywhere, or finite almost everywhere, respectively; and in the latter case, such operators are bounded from $BMO(\R^n)$ to $BLO(\R^n)$, which improve and generalize some previous results.

Keywords: generalized Littlewood-Paley operators, $BMO$ spaces, $BLO$ spaces

MSC numbers: 42B20, 42B25, 42B35, 42B99

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