Square area integral estimates for subharmonic functions in NTA domains

Abstract

In this paper, we prove a good-λ inequality between the nontangential maximal function and the square area integral of a subharmonic function u in a bounded NTA domain D in Rⁿ. We achieve this by showing that a weighted Riesz measure of u is a Carleson measure, with the Carleson norm bounded by a constant independent of u. As consequences of the good-λ inequality, we obtain McConnell-Uchiyama's inequality and an analogue of Murai-Uchiyama's inequality for subharmonic functions in D.