Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T00:47:20.817Z Has data issue: false hasContentIssue false
  • English
  • Français

Covering lemmas revisited

Published online by Cambridge University Press:  20 January 2009

Anthony Carbery
Anthony Carbery
Affiliation:
Mathematics DivisionUniversity of SussexFalmerBrighton BN1 9QH
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note we intend to discuss the method of A. Córdoba and R. Fefferman of using covering lemmas to control maximal functions, and make some simplifications which allow us to obtain alternative proofs of some of their results.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 1 , February 1988 , pp. 145 - 150
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

1.Carbery, A., Chang, S.-Y. A. and Garnett, J., Weights and L log L, Pacific J. Math. 120 (1985), 33–45.CrossRefGoogle Scholar
2.Córdoba, A., The Kakeya maximal function and the spherical summation multipliers, Amer. J. Math. 99 (1977), 1–22.CrossRefGoogle Scholar
3.Córdoba, A. and Fefferman, R., A geometric proof of the strong maximal theorem, Ann. of Math. 102 (1975), 95–100.Google Scholar
4.Córdoba, A. and Fefferman, R., On differentiation of integrals, Proc. Nat. Acad. Sci. U.S.A. 74(1977), 2211–2213.CrossRefGoogle ScholarPubMed
5.Hardy, G. H. and Littlewood, J. E., A maximal theorem with function-theoretic applications, Acta Math. 54 (1930), 81–116.CrossRefGoogle Scholar
6.Jawerth, B., Weighted inequalities for maximal operators: Linearization, localization factorization, Amer. J. Math., 108 (1986), 361–414.CrossRefGoogle Scholar
7.Nagel, A., Stein, E. M. and Wainger, S., Differentiation in lacunary directions, Proc. Nat. Acad., Sci. U.S.A. 75 (1978), 1060–1062.CrossRefGoogle ScholarPubMed
8.Sawyer, E., Two Weight Norm Inequalities for certain Maximal and Integral Operators (Springer Lecture Notes in Math. 908 1982), 102–127.Google Scholar