A covering lemma for rectangles in ℝⁿ

Fefferman, Robert; Pipher, Jill

doi:10.1090/S0002-9939-05-07902-5

A covering lemma for rectangles in ${\mathbb {R}}^n$
HTML articles powered by AMS MathViewer

by Robert Fefferman and Jill Pipher

Proc. Amer. Math. Soc. 133 (2005), 3235-3241

DOI: https://doi.org/10.1090/S0002-9939-05-07902-5

Published electronically: June 20, 2005

PDF | Request permission

Abstract:

We prove a covering lemma for rectangles in ${\mathbb {R}}^n$ which has connections to a problem of Zygmund and its solution in three dimensions by Cordoba.

References

Sun-Yung A. Chang and Robert Fefferman, Some recent developments in Fourier analysis and $H^p$-theory on product domains, Bull. Amer. Math. Soc. (N.S.) 12 (1985), no. 1, 1–43. MR 766959, DOI 10.1090/S0273-0979-1985-15291-7
Antonio Córdoba, Maximal functions, covering lemmas and Fourier multipliers, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978) Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979, pp. 29–50. MR 545237
A. Cordoba and R. Fefferman, A geometric proof of the strong maximal theorem, Ann. of Math. (2) 102 (1975), no. 1, 95–100. MR 379785, DOI 10.2307/1970976
R. Fefferman and J. Pipher, Multiparameter operators and sharp weighted inequalities, Amer. J. Math. 119 (1997), no. 2, 337–369. MR 1439553, DOI 10.1353/ajm.1997.0011
F. Ricci and E. M. Stein, Multiparameter singular integrals and maximal functions, Ann. Inst. Fourier (Grenoble) 42 (1992), no. 3, 637–670 (English, with English and French summaries). MR 1182643, DOI 10.5802/aif.1304
Fernando Soria, Examples and counterexamples to a conjecture in the theory of differentiation of integrals, Ann. of Math. (2) 123 (1986), no. 1, 1–9. MR 825837, DOI 10.2307/1971350