BOUNDEDNESS OF THE FRACTIONAL INTEGRAL OPERATOR WITH ROUGH KERNEL AND ITS COMMUTATOR IN VANISHING GENERALIZED VARIABLE EXPONENT MORREY SPACES ON UNBOUNDED SETS

In this paper, we study the boundedness of fractional integral operators and their commutators in vanishing generalized Morrey spaces with variable exponent on unbounded sets. Using the properties of variable exponent functions and the pointwise estimates of operators TΩ, α and their commutators[b, TΩ, α] in Lebesgue spaces with variable exponent, we obtain the boundedness of fractional integral operators TΩ, α and their commutators[b, TΩ, α] in vanishing generalized Morrey spaces with variable exponents on unbounded sets, which extend the previous results.