We find conditions on the variable parameters p ( x ) , q ( t ) and α ( t ) , defining the Herz space H p ( · ) , q ( · ) , α ( · ) ( R n ) , 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).