Revista de la
Unión Matemática Argentina
Pointwise convergence of fractional powers of Hermite type operators
Guillermo Flores, Gustavo Garrigós, Teresa Signes, and Beatriz Viviani
Volume 66, no. 1 (2023), pp. 187–205    

https://doi.org/10.33044/revuma.4357

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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 $L^\sigma f(x_0)$ 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 $(-\Delta+R)^\sigma$, with $R > 0$.

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