The Riemann boundary value problem in the class of Cauchy type integrals with densities of grand variable exponent Lebesgue spaces

Abstract The present paper deals with the Riemann boundary value problem for analytic functions in the framework of the new function spaces introduced by the first two authors, the so-called grand variable exponent Lebesgue spaces which unify two non-standard type function spaces: variable exponent Lebesgue spaces and grand Lebesgue spaces.