Abstract
In this paper we consider global Morrey spaces with variable exponents p(.), θ(.), where is an unbounded set. The questions of boundedness of the singular integral operator and its commutator in these spaces are investigated. We give the conditions for the variable exponent and for the functions ( (.), (.)) under which the singular integral operator will be bounded from to . The same conditions for the boundedness of the commutator of the singular integral operator in these spaces are obtained.. In the case when the exponents are constant numbers, the questions of boundedness of the singular integral operator and its commutator in global spaces were previously studied by other authors. There are also well-known results on the boundedness of a singular integral operator in the global Morrey-type spaces with variable exponents when the set is bounded.