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

Abstract

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 $B_{\nu }$ in the exotic range of the parameter $-\infty <\nu <1$. 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).

31 pages

Cited by in corpus (2)

• Endpoint estimates and optimality for the generalized spherical maximal operator on radial functions
• Variation operators for semigroups associated with Fourier-Bessel expansions