Pointwise convergence of fractional powers of Hermite type operators

Guillermo Flores; Gustavo Garrigos; Teresa Signes; Beatriz Viviani

Pointwise convergence of fractional powers of Hermite type operators

Analysis of PDEs 2023-03-21 v2

Authors: Guillermo Flores , Gustavo Garrigos , Teresa Signes , Beatriz Viviani

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 $R>0$ .

Keywords

fractional powers Hermite operator Ornstein-Uhlenbeck operator pointwise convergence minimal smoothness conditions

Cite

@article{arxiv.2211.06359,
  title  = {Pointwise convergence of fractional powers of Hermite type operators},
  author = {Guillermo Flores and Gustavo Garrigos and Teresa Signes and Beatriz Viviani},
  journal= {arXiv preprint arXiv:2211.06359},
  year   = {2023}
}

Comments

19 pages. This paper is dedicated to the memory of Eleonor (Pola) Harboure. Revised version, to appear in Rev Uni\'on Matem Argentina

Pointwise convergence of fractional powers of Hermite type operators

Abstract

Keywords

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