weights for nondoubling measures in and applications

Authors:
Joan Orobitg and Carlos Pérez

Journal:
Trans. Amer. Math. Soc. **354** (2002), 2013-2033

MSC (2000):
Primary 42B25, 42B20

DOI:
https://doi.org/10.1090/S0002-9947-02-02922-7

Published electronically:
January 11, 2002

MathSciNet review:
1881028

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Abstract: We study an analogue of the classical theory of weights in without assuming that the underlying measure is doubling. Then, we obtain weighted norm inequalities for the (centered) Hardy-Littlewood maximal function and corresponding weighted estimates for nonclassical Calderón-Zygmund operators. We also consider commutators of those Calderón- Zygmund operators with bounded mean oscillation functions (), extending the main result from R. Coifman, R. Rochberg, and G. Weiss, *Factorization theorems for Hardy spaces in several variables*, Ann. of Math. **103** (1976), 611-635. Finally, we study self-improving properties of Poincaré-B.M.O. type inequalities within this context; more precisely, we show that if is a locally integrable function satisfying for all cubes , then it is possible to deduce a higher integrability result for , assuming a certain simple geometric condition on the functional .

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Additional Information

**Joan Orobitg**

Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bella- terra, Spain

Email:
orobitg@mat.uab.es

**Carlos Pérez**

Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madird, 28049 Madrid, Spain

Address at time of publication:
Department of Mathematical Analysis, Universidad de Sevilla, 41080 Sevilla, Spain

Email:
carlos.perez@uam.es

DOI:
https://doi.org/10.1090/S0002-9947-02-02922-7

Received by editor(s):
February 23, 2000

Received by editor(s) in revised form:
September 12, 2000

Published electronically:
January 11, 2002

Additional Notes:
The first author’s research was partially supported by CIRIT grant 2000 SGR00059 and by DGICYT grant BFM 2000-0361, Spain.

The second author’s research was partially supported by DGESIC grant PB98-0106, Spain.

Article copyright:
© Copyright 2002
American Mathematical Society