Weighted iterates and variants of the Hardy-Littlewood maximal operator

Leckband, M. A.; Neugebauer, C. J.

doi:10.1090/S0002-9947-1983-0704601-7

Weighted iterates and variants of the Hardy-Littlewood maximal operator
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by M. A. Leckband and C. J. Neugebauer PDF

Trans. Amer. Math. Soc. 279 (1983), 51-61 Request permission

Abstract:

In a recent paper, M. A. Leckband and C. J. Neugebauer obtained a rearrangement inequality for a generalized maximal operator with respect to two measures. For an application they studied norm bounds for the iterated Hardy-Littlewood maximal operator with respect to two measures. In this paper this theory is further developed and other applications of the rearrangement inequality are obtained.

References

Lennart Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. of Math. (2) 76 (1962), 547–559. MR 141789, DOI 10.2307/1970375
Richard A. Hunt, On $L(p,\,q)$ spaces, Enseign. Math. (2) 12 (1966), 249–276. MR 223874
Huann Ming Chung, Richard A. Hunt, and Douglas S. Kurtz, The Hardy-Littlewood maximal function on $L(p,\,q)$ spaces with weights, Indiana Univ. Math. J. 31 (1982), no. 1, 109–120. MR 642621, DOI 10.1512/iumj.1982.31.31012
W. B. Jurkat and J. L. Troutman, Maximal inequalities related to generalized a.e. continuity, Trans. Amer. Math. Soc. 252 (1979), 49–64. MR 534110, DOI 10.1090/S0002-9947-1979-0534110-9

Restricted weak type inequalities with weights

M. A. Leckband and C. J. Neugebauer, A general maximal operator and the $A_{p}$-condition, Trans. Amer. Math. Soc. 275 (1983), no. 2, 821–831. MR 682735, DOI 10.1090/S0002-9947-1983-0682735-3
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
Benjamin Muckenhoupt and Richard L. Wheeden, Two weight function norm inequalities for the Hardy-Littlewood maximal function and the Hilbert transform, Studia Math. 55 (1976), no. 3, 279–294. MR 417671, DOI 10.4064/sm-55-3-279-294
E. M. Stein, Editor’s note: the differentiability of functions in $\textbf {R}^{n}$, Ann. of Math. (2) 113 (1981), no. 2, 383–385. MR 607898
Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095