Riesz transforms associated with the Neumann Laplacian

• Zhang, Juan ^[1]
  1. [1] Beijing Forestry University

     Beijing Forestry University

     China

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 77, Fasc. 3, 2026, págs. 765-789
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper, we investigate the weighted theory of Riesz transforms R_{{\Delta _N}} associated with the Neumann Laplacian and its commutator C_b(R_{{\Delta _N}}). The main goal is to show weighted compactness of C_b(R_{{\Delta _N}}) on L^p(w) for any p \in (1, \infty ), w \in A_{p, {\Delta _N}}, and b \in \operatorname {CMO}_{{\Delta _N}}(\mathbb {R}^n). To achieve this, we establish sharp weighted estimates, weighted endpoint estimates, local decay estimates for R_{{\Delta _N}} and C_b(R_{{\Delta _N}}). Moreover, we introduce the Hardy-Littlewood maximal operator associated with the Neumann Laplacian in order to characterize A_{p, {\Delta _N}} weights class. Beyond that, we give Rubio de Francia extrapolation theorems to prove weighted compactness of C_b(R_{{\Delta _N}}).