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arXiv · 2211.06359

Pointwise convergence of fractional powers of Hermite type operators

Guillermo Flores·Gustavo Garrigos·Teresa Signes·Beatriz Viviani
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Abstract

When $L$ is the Hermite or the Ornstein-Uhlenbeck operator, we find minimal integrability and smoothness conditions on a function $f$ so that the fractional power $L^σf(x_0)$ is well-defined at a given point $x_0$. We illustrate the optimality of the conditions with various examples. Finally, we obtain similar results for the fractional operators $(-Δ+R)^σ$, with $R>0$.

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Guillermo Flores, Gustavo Garrigos, Teresa Signes, Beatriz Viviani. 2023-03-20. Pointwise convergence of fractional powers of Hermite type operators. https://arxiv.org/abs/2211.06359

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