On the variation of the Hardy–Littlewood maximal functions on finite graphs

• Liu, Feng ^[1] ; Xue, Qingying ^[2]
  1. [1] Shandong University of Science and Technology

     Shandong University of Science and Technology

     China

     
  2. [2] Beijing Normal University

     Beijing Normal University

     China

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 72, Fasc. 2, 2021, págs. 333-349
• Idioma: inglés
• DOI: 10.1007/s13348-020-00290-6
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let G be a connected and finite graph with the set of vertices V and the set of edges E. Let MG be the Hardy–Littlewood maximal function defined on graph G and Mα,G (0≤α<1) be its fractional version. In this paper, the regularity problems related to MG and Mα,G will be studied. We show that MG:BVp(G)→BVp(G) is bounded and Mα,G:ℓp(V)→BVq(G) is bounded and continuous for all 0