On Hardy-Littlewood and Fefferman-Stein strong maximal functions
The estimate \[ (M_s f)^*(t)\leq c(f^\#_s)^*(t/2)+f^*(2t) \] is proved, where \(M_s f\) and \(f^\#_s\) are the Hardy-Littlewood and the Fefferman-Stein strong maximal functions, respectively, and \((.)^*\) denotes nonincreasing permutation. Similar estimate for usual maximal functions implies the Fefferman-Stein theorem [see \textit{R. A. DeVore} and \textit{R. C. Sharpley}, Mem. Am. Math. Soc. 293, 115 p. (1984; Zbl 0529.42005)].
strong Hardy-Littlewood maximal function
scientific article; zbMATH DE number 1158917