Estimates for Littlewood-Paley operators in BMO(R-n)

摘要

Let g(f) be the Littlewood-Paley g-function of f on R-n. In this paper, the authors prove that if f is an element of BMO(R-n) (the space of functions with bounded mean oscillation), then g(f) is either infinite everywhere or finite almost everywhere, and in the latter case, [g(f)](2) is bounded from BMO(R-n) into BLO(R-n) (the space of functions with bounded lower oscillation), which is a proper subspace of BMO(R-n). Moreover, the authors also establish similar results for the Lusin-area function and the Littlewood-Paley g(lambda)*-function. (c) 2008 Elsevier Inc. All rights reserved.