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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Paraexponentials, Muckenhoupt weights,
and resolvents of paraproducts


Authors: María C. Pereyra and Lesley A. Ward
Journal: Proc. Amer. Math. Soc. 126 (1998), 135-144
MSC (1991): Primary 42B99; Secondary 47A10
MathSciNet review: 1452819
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Abstract: We analyze the stability of Muckenhoupt's $\bold{ RH} ^d_p$ and $\bold{ A} _p^d$ classes of weights under a nonlinear operation, the $\lambda $-operation. We prove that the dyadic doubling reverse Hölder classes $\bold{ RH} ^d_p$ are not preserved under the $\lambda $-operation, but the dyadic doubling $A_p$ classes $\bold{ A} _p^d$ are preserved for $0\leq \lambda \leq 1$. We give an application to the structure of resolvent sets of dyadic paraproduct operators.


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Additional Information

María C. Pereyra
Affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131-1141
Email: crisp@math.unm.edu

Lesley A. Ward
Affiliation: Department of Mathematics, Harvey Mudd College, Claremont, California 91711
Email: lesley@math.rice.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04400-1
PII: S 0002-9939(98)04400-1
Keywords: Muckenhoupt weights, reverse H\"older $RH_p$, $A_p$, doubling weights, dyadic paraproducts, paraexponentials
Received by editor(s): May 9, 1996
Additional Notes: This research was supported in part by (CP) NSF grant #DMS-93-04580 and (LW) at MSRI by NSF grant #DMS-90-22140.
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1998 American Mathematical Society