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arXiv · 1209.6133

Riesz Potentials, Bessel Potentials and Fractional Derivatives on Triebel-Lizorkin spaces for the Gaussian Measure

A. Eduardo Gatto·Ebner Pineda·Wilfredo Urbina
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Abstract

In a previous paper the boundedness properties of Riesz Potentials, Bessel potentials and Fractional Derivatives were studied in detail on Gaussian Besov-Lipschitz spaces $B_{p,q}^α(γ_d)$. In this paper we will continue our study proving the boundedness of those operators on Gaussian Triebel-Lizorkin spaces $F_{p,q}^α(γ_d)$. Also these results can be extended to the case of Laguerre or Jacobi expansions and even further to the general framework of diffusions semigroups.

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A. Eduardo Gatto, Ebner Pineda, Wilfredo Urbina. 2012-09-27. Riesz Potentials, Bessel Potentials and Fractional Derivatives on Triebel-Lizorkin spaces for the Gaussian Measure. https://arxiv.org/abs/1209.6133

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