Paraexponentials, Muckenhoupt weights, and resolvents of paraproducts
Cristina Pereyra, Lesley Ward
Abstract
We analyze the stability of Muckenhoupt's and classes of weights under a nonlinear operation, the -operation. We prove that the dyadic doubling reverse Hölder classes are not preserved under the -operation, but the dyadic doubling Ap classes are preserved for 0< <1. We give an application to the structure of resolvent sets of dyadic paraproduct operators.
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