Riesz potential operator in continual variable exponents Herz spaces

We find conditions on the variable parameters p(x),q(t) and α(t), defining the Herz space Hp(·),q(·),α(·)(Rn), for the validity of Sobolev type theorem for the Riesz potential operator to be bounded within the frameworks of such variable exponents Herz spaces. We deal with a "continual" version of Herz spaces (which coincides with the "discrete" one when q is constant).