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

Research paper by Adam Nowak, Luz Roncal

Indexed on: 24 Nov '11Published on: 24 Nov '11Published in: Mathematics - Classical Analysis and ODEs



Abstract

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.