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

We prove sharp power-weighted L-p, weak type and restricted weak type inequalities for the heat semigroup maximal operator and Riesz transforms associated with the Bessel operator B-v in the exotic range of the parameter -infinity < v < 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). (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This study demonstrates sharp power-weighted L-p, weak type, and restricted weak type inequalities for the heat semigroup maximal operator and Riesz transforms associated with the Bessel operator B-v in the exotic parameter range -infinity < v < 1. Furthermore, it characterizes basic mapping properties for other fundamental harmonic analysis operators, including the heat semigroup based vertical g-function and fractional integrals (Riesz potential operators) within the same framework.