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 $ν$ is half-integer. Moreover, still for half-integer $ν$, we also obtain sharp estimates of all kernels subordinated to the heat kernel. Analogous estimates for general $ν> -1$ are conjectured. Some consequences concerning the related heat semigroup maximal operator are discussed.

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