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

摘要

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.