Paraexponentials, Muckenhoupt weights, and resolvents of paraproducts

We analyze the stability of Muckenhoupt's RHpd and A(p)(d) classes of weights under a nonlinear operation, the lambda-operation. We prove that the dyadic doubling reverse Holder classes RHpd are not preserved under the lambda operation, but the dyadic doubling A(p) classes A(p)(d) are preserved for 0 less than or equal to lambda less than or equal to 1. We give an application to the structure of resolvent sets of dyadic paraproduct operators.