Extensions of Rubio de Francia's extrapolation theorem in variable Lebesgue space and application

Abstract: We obtain one variant of the extrapolation theorem of Rubio de Fracia for variable exponent Lebesgue spaces. As a consequence we obtain conditions guarantee boundedness of strongly singular integral operators, singular integral operators with rough kernels, fractional maximal operators related to spherical means, Bochner-Riesz operators in variable Lebesgue spaces.