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Weighted Maximal Inequalities for ℓr- Valued Functions

Published online by Cambridge University Press:  20 November 2018

H. P. Heinig
H. P. Heinig*
Affiliation:
McMaster UniversityHamilton, Ontario, Canada
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C. Feffermann and E. M. Stein [2] have shown that the continuity property of the Hardy-Littlewood maximal functions between Lp-spaces, 1 < p < ∞, extends to ℓr-valued functions on ℝn. Specifically, if f = (f1, f2,…) is a sequence of functions defined on Rn, let for l<∞, |f(x)|r be given by

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 4 , 01 December 1976 , pp. 445 - 453
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Fefferman, C. and Coifman, R. R.; Weighted Norm Inequalities for Maximal Functions and Singular Integrals, Studia Math. 51 (1974) pp. 241–250.Google Scholar
2. Fefferman, C., Coifman, R. R. and Stein, E. M., Some Maximal Inequalities, Amer. J. Math. (1971) pp. 107–115.Google Scholar
3. Heinig, H. P., Some Extensions of Hardy’s Inequality, SIAM J. Math. Anal. 6, No. 4 (1975) pp. 698–713.Google Scholar
4. Hewitt, E. and Stromberg, K., Real and Abstract Analysis, Springer Verl. N.Y. 1965.Google Scholar
5. Muckenhoupt, B., Weighted Norm Inequalities for the Hardy Maximal Function, Trans. Amer. Math. Soc. 165 (1972) pp. 207–226.Google Scholar
6. Muckenhoupt, B., Hardy’s Inequality with Weights, Studia Math. 44 (1972) pp. 31–38.Google Scholar
7. Muckenhoupt, B., The Equivalence of Two Conditions for Weighted Functions, Studia Math. 49 (1974) pp. 101–106.Google Scholar