Regularization of weights

Authors:
Richard J. Bagby and Basem Masaedeh

Journal:
Proc. Amer. Math. Soc. **131** (2003), 761-764

MSC (2000):
Primary 42B25

Published electronically:
October 15, 2002

MathSciNet review:
1937414

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Abstract | References | Similar Articles | Additional Information

Abstract: We show how to approximate a given weight function in the class by weights that are bounded above by multiples of their infima in such a way that the constant is not increased. As an application, we show that the precise range of for which a given weight is in cannot be determined by extrapolating the constants.

**1.**Richard J. Bagby and Basem Masaedeh,*Optimal extrapolation of weight conditions*, Panamer. Math. J.**7**(1997), no. 1, 55–63. MR**1427020****2.**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**, 10.1512/iumj.1982.31.31012**3.**R. R. Coifman and C. Fefferman,*Weighted norm inequalities for maximal functions and singular integrals*, Studia Math.**51**(1974), 241–250. MR**0358205****4.**F. W. Gehring,*The 𝐿^{𝑝}-integrability of the partial derivatives of a quasiconformal mapping*, Acta Math.**130**(1973), 265–277. MR**0402038****5.**Benjamin Muckenhoupt,*Weighted norm inequalities for the Hardy maximal function*, Trans. Amer. Math. Soc.**165**(1972), 207–226. MR**0293384**, 10.1090/S0002-9947-1972-0293384-6

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Additional Information

**Richard J. Bagby**

Affiliation:
Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003

Email:
rbagby@nmsu.edu

**Basem Masaedeh**

Affiliation:
Department of Mathematics, Mu’tah University, Mu’tah, Jordan

Email:
basmas_59@yahoo.com

DOI:
http://dx.doi.org/10.1090/S0002-9939-02-06861-2

Received by editor(s):
September 12, 2001

Published electronically:
October 15, 2002

Communicated by:
Andreas Seeger

Article copyright:
© Copyright 2002
American Mathematical Society