Paraexponentials, Muckenhoupt weights, and resolvents of paraproducts

Details Paraexponentials, Muckenhoupt weights, and resolvents of paraproducts Paraexponentials, Muckenhoupt weights, and resolvents of paraproducts

1996-04-29

arxiv.org/abs/math/9604229v1

Mathematics

Functional Analysis

Scientific paper

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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