Local integrability of strong and iterated maximal functions
Let denote the strong maximal operator. Let and denote the one-dimensional Hardy-Littlewood maximal operators in the horizontal and vertical directions in ℝ². A function h supported on the unit square Q = [0,1]×[0,1] is exhibited such that but . It is shown that if f is a function supported on Q such that but , then there exists a set A of finite measure in ℝ² such that .