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Paraexponentials, Muckenhoupt weights, and resolvents of paraproducts

Authors:	Marí a C Pereyra Lesley A Ward

Institution:	Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131-1141 ; Department of Mathematics, Harvey Mudd College, Claremont, California 91711

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 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.

Keywords:	Muckenhoupt weights reverse H\"older $RH_p$ $A_p$ doubling weights dyadic paraproducts paraexponentials

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