On sharp heat and subordinated kernel estimates in the Fourier-Bessel setting

We prove qualitatively sharp heat kernel bounds in the setting of Fourier-Bessel expansions when the associated type parameter $\nu$ is half-integer. Moreover, still for half-integer $\nu$, we also obtain sharp estimates of all kernels subordinated to the heat kernel. Analogous estimates for general $\nu >-1$ are conjectured. Some consequences concerning the related heat semigroup maximal operator are discussed.