Pointwise convergence of fractional powers of Hermite type operators

  1. Guillermo Flores 1
  2. Gustavo Garrigós 2
  3. Teresa Signes 2
  4. Beatriz Viviani 3
  1. 1 Universidad Nacional de Córdoba, Argentina
  2. 2 Universidad de Murcia, España
  3. 3 Universidad Nacional del Litoral, Argentina
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Journal:
Revista de la Unión Matemática Argentina

ISSN: 1669-9637,  0041-6932

Year of publication: 2023

Volume: 66

Issue: 1

Pages: 187-205

Type: Article

DOI: 10.33044/REVUMA.4357 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Revista de la Unión Matemática Argentina

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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 Lσf(x0) is well-defined at a given point x0. We illustrate the optimality of the conditions with various examples. Finally, we obtain similar results for the fractional operators (−∆ + R) σ, with R > 0.

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