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Paraexponentials, Muckenhoupt weights, and resolvents of paraproducts

Cristina Pereyra·Lesley Ward
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Abstract

We analyze the stability of Muckenhoupt's $\RHp$ and $\Ap$ classes of weights under a nonlinear operation, the $\lb$-operation. We prove that the dyadic doubling reverse H\"older classes $\RHp$ are not preserved under the $\lb$-operation, but the dyadic doubling $A_p$ classes $\Ap$ are preserved for $0<\lb <1$. We give an application to the structure of resolvent sets of dyadic paraproduct operators.

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BibTeXRIS

Cristina Pereyra, Lesley Ward. 1996-04-29. Paraexponentials, Muckenhoupt weights, and resolvents of paraproducts. https://doi.org/10.1090/s0002-9939-98-04400-1

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