Conditions for the imbedding of the function class $W_f^1(G,\,A)$ in the space $C(G)$

The function class $W_f^1(G,A)$ is defined. A general problem concerning necessary and sufficient conditions under which this class can be imbedded in the space $C(G)$ of functions continuous on $G$ is posed, and the special case of this problem in which the function $f(x_1,x_2,\dots,x_n)$, involved in the definition of $W_f^1(G,A)$ on $|x|=\sqrt{x_1^2+x_2^2+\dots+x_n^2}$ is solved.