PARAEXPONENTIALS, MUCKENHOUPT WEIGHTS, AND RESOLVENTS OF PARAPRODUCTS

CRISTINA PEREYRA LESLEY WARD

Abstract. We analyze the stability of Muckenhoupt’s RH_{p}^{d} and A_{p}^{d} classes of weights under a nonlinear operation, the λ-operation. We prove that the dyadic doubling reverse Hölder classes RH_{p}^{d} are not preserved under the λ-operation, but the dyadic doubling A_{p} classes A_{p}^{d} are preserved for 0 < λ < 1. We give an application to the structure of resolvent sets of dyadic paraproduct operators.