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Regularization of $A_{p}$ weights

Author(s): Richard J. Bagby; Basem Masaedeh
Journal: Proc. Amer. Math. Soc. 131 (2003), 761-764.
MSC (2000): Primary 42B25
Posted: October 15, 2002
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Abstract: We show how to approximate a given weight function in the class $A_{p}$ by weights that are bounded above by multiples of their infima in such a way that the $A_{p}$ constant is not increased. As an application, we show that the precise range of for which a given weight is in $A_{p}$ cannot be determined by extrapolating the $A_{p}$ constants.

References:

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2.: H.-M. Chung, R. A. Hunt, and D. S. Kurtz, The Hardy-Littlewood maximal function on L(p,q) spaces with weights, Indiana Univ. Math. J. 31 (1982), 109-120. MR 83b:42021
3.: R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250. MR 50:10670
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5.: B. Muckenhoupt, Weighted inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226. MR 45:2461


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