Abstract

Córdoba–Fefferman collections are defined and used to characterize functions whose corresponding maximal functions are locally integrable. Córdoba–Fefferman collections are also used to show that, if M_x and M_y respectively denote the one-dimensional Hardy–Littlewood maximal operators in the horizontal and vertical directions in R², M_HL denotes the standard Hardy–Littlewood maximal operator in R², and f is a measurable function supported in the unit square Q = [0,1] × [0,1], then ∫ _QM_HLf ∼∫ _QM_xf + ∫ _QM_yf.

Authors