Vertical Littlewood–Paley functions related to a Schrödinger operator

• Bruno Bongioanni ^[1] ; Eleonor Harboure ^[1] ; Pablo Quijano ^[1]
  1. [1] CONICET-UNL, Argentina
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 66, Nº. 1, 2023, págs. 117-139
• Idioma: inglés
• DOI: 10.33044/revuma.4381
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• Resumen

  • In this work we consider the Littlewood–Paley quadratic function associated to the Schr¨odinger operator L = −∆ + V involving spatial derivatives of the semigroup’s kernel. Under an appropriate reverse-H¨older condition on the potential we show boundedness on weighted Lp spaces for 1 < p < p0, where p0 depends on the order of the reverse-H¨older property. Using a subordination formula we extend these results to the corresponding quadratic function associated to the semigroup related to Lα, 0 < α < 1.