Covering lemmas and the sharp function
HTML articles powered by AMS MathViewer
- by Richard J. Bagby and Douglas S. Kurtz PDF
- Proc. Amer. Math. Soc. 93 (1985), 291-296 Request permission
Abstract:
We present some new measure-theoretic inequalities for families of cubes covering open sets in ${{\mathbf {R}}^n}$ and use these inequalities to estimate the Hardy-Littlewood maximal function $Mf$ in terms of the sharp function ${f^\# }$.References
-
R. J. Bagby and D. S. Kurtz, A rearranged good $\lambda$ inequality, preprint.
- Colin Bennett, Ronald A. DeVore, and Robert Sharpley, Weak-$L^{\infty }$ and BMO, Ann. of Math. (2) 113 (1981), no. 3, 601–611. MR 621018, DOI 10.2307/2006999
- Colin Bennett and Robert Sharpley, Weak-type inequalities for $H^{p}$ and BMO, 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. 201–229. MR 545259
- R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241–250. MR 358205, DOI 10.4064/sm-51-3-241-250
- C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193. MR 447953, DOI 10.1007/BF02392215
- F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415–426. MR 131498, DOI 10.1002/cpa.3160140317
- Benjamin Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207–226. MR 293384, DOI 10.1090/S0002-9947-1972-0293384-6
- Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 291-296
- MSC: Primary 42B25; Secondary 46E30
- DOI: https://doi.org/10.1090/S0002-9939-1985-0770539-X
- MathSciNet review: 770539