# POINTWISE ESTIMATES AND BOUNDEDNESS OF GENERALIZED LITTLEWOOD-PALEY OPERATORS IN BMO(ℝn)

• Wu, Yurong ;
• Wu, Huoxiong
• Published : 2015.05.31
• 32 15

#### Abstract

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($\mathbb{R}^n$) to BLO($\mathbb{R}^n$), which improve and generalize some previous results.

#### Keywords

generalized Littlewood-Paley operators;BMO spaces;BLO spaces

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#### Acknowledgement

Supported by : NNSF