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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.

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