Pointwise convergence of fractional powers of Hermite type operators
DOI:
https://doi.org/10.33044/revuma.4357Abstract
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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Copyright (c) 2023 Guillermo Flores, Gustavo Garrigós, Beatriz Viviani, Teresa Signes
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