Córdoba–Fefferman collections in harmonic analysis

Paul Alton Hagelstein

Vol. 216 (2004), No. 1, 95–109

DOI: 10.2140/pjm.2004.216.95

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.

Milestones

Received: 9 June 2000

Published: 1 September 2004