Long, Ruilin; Shen, Zhongwei A note on a covering lemma of A. Cordoba and R. Fefferman. (English) Zbl 0671.42019 Chin. Ann. Math., Ser. B 9, No. 3, 283-291 (1988). Summary: This note simplifies Cordoba-Fefferman’s proof on the weak boundedness of strong maximal operator \(M_ s\) (with respect to \(d\mu)\) on \(L(1+\log^{+(n-1)}L)\). Some two-weighted boundedness results on \(L(1+\log^{+\alpha}L)\) of \(M_ s\) are investigated. Cited in 4 Documents MSC: 42B25 Maximal functions, Littlewood-Paley theory Keywords:weak boundedness; strong maximal operator; two-weighted boundedness PDFBibTeX XMLCite \textit{R. Long} and \textit{Z. Shen}, Chin. Ann. Math., Ser. B 9, No. 3, 283--291 (1988; Zbl 0671.42019)