On weighted compactness of commutators of square function and semi-group maximal function associated to Schrödinger operators

• Wang, Shifen ^[1] ; Zhang, Chunmei ^[1] ; Xue, Qingying ^[1]
  1. [1] Beijing Normal University

     Beijing Normal University

     China

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 1, 2024, págs. 129-148
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let be the Laplacian operator on and V be a nonnegative potential satisfying an appropriate reverse Hölder inequality. The Littlewood–Paley square function g associated with the Schrödinger operator is defined by:

    In this paper, we show that the commutators of g are compact operators on for if θ ρ and ρ θ , where θ ρ denotes the closure of in the θ ρ topology and ρ θ is a weighted class which is more larger than Muckenhoupt weight class. An extra weight condition in a previous weighted compactness result is removed for the commutators of the semi-group maximal function defined by