Mapping properties of fundamental harmonic analysis operators in the exotic Bessel framework

Abstract

We prove sharp power-weighted Lp, weak type and restricted weak type inequalities for the heat semigroup maximal operator and Riesz transforms associated with the Bessel operator Bν in the exotic range of the parameter −∞<ν<1. Moreover, in the same framework, we characterize basic mapping properties for other fundamental harmonic analysis operators, including the heat semigroup based vertical g-function and fractional integrals (Riesz potential operators).