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Boundedness of commutators of singular and potential operators in generalized grand Morrey spaces and some applications

Tom 217 / 2013

Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro Studia Mathematica 217 (2013), 159-178 MSC: Primary 42B20; Secondary 42B25, 42B35. DOI: 10.4064/sm217-2-4

Streszczenie

In the setting of spaces of homogeneous type, it is shown that the commutator of Calderón–Zygmund type operators as well as the commutator of a potential operator with a BMO function are bounded in a generalized grand Morrey space. Interior estimates for solutions of elliptic equations are also given in the framework of generalized grand Morrey spaces.

Autorzy

  • Vakhtang KokilashviliDepartment of Mathematical Analysis
    A. Razmadze Mathematical Institute
    I. Javakhishvili Tbilisi State University
    2, University St.
    0186 Tbilisi, Georgia
    and
    International Black Sea University
    3, Agmashenebeli Ave.
    0131 Tbilisi, Georgia
    e-mail
  • Alexander MeskhiDepartment of Mathematical Analysis
    A. Razmadze Mathematical Institute
    I. Javakhishvili Tbilisi State University
    2, University St.
    0186 Tbilisi, Georgia
    and
    Department of Mathematics
    Faculty of Informatics and Control Systems
    Georgian Technical University
    77, Kostava St.
    Tbilisi, Georgia
    e-mail
  • Humberto RafeiroPontificia Universidad Javeriana
    Departamento de Matemáticas
    Cra 7a No 43-82
    Ed. Carlos Ortiz 604
    Bogotá, Colombia
    and
    Instituto Superior Técnico
    Departamento de Matemática
    Centro CEAF
    Av. Rovisco Pais
    1049-001 Lisboa, Portugal
    e-mail

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