On degree of approximation of the Gauss-Weierstrass means for smooth L-p(R-n) functions

The notion of mu-smooth point of an L-p(R-n)-function f is introduced in terms of some 'maximal function.' Then the connection between the order of mu-smoothness of the function f and the rate of convergence of the Gauss-Weierstrass means to f, when epsilon tends to 0, is obtained.