Geodesic
Boundedness of commutators of singular and potential operators in generalized grand Morrey spaces and some applications
Vakhtang Kokilashvili 1   ; Alexander Meskhi 2   ; Humberto Rafeiro 3
1 Department 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
2 Department 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
3 Pontificia 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
Studia Mathematica, Tome 217 (2013) no. 2, pp. 159-178 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm217-2-4
Keywords: setting spaces homogeneous type shown commutator calder zygmund type operators commutator potential operator bmo function bounded generalized grand morrey space interior estimates solutions elliptic equations given framework generalized grand morrey spaces

Vakhtang Kokilashvili  1   ; Alexander Meskhi  2   ; Humberto Rafeiro  3

1 Department 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
2 Department 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
3 Pontificia 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 
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     title = {Boundedness of commutators of singular
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Vakhtang Kokilashvili; Alexander Meskhi; Humberto Rafeiro. Boundedness of commutators of singular
 and potential operators in generalized grand Morrey spaces and some applications. Studia Mathematica, Tome 217 (2013) no. 2, pp. 159-178. doi: 10.4064/sm217-2-4

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