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

Shifen Wang, Chunmei Zhang, Qingying Xue

• 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