On embedding in classes of continuous functions of several variables

P. L. Ul'yanov (RZhMat., 1968, 5B120) has found necessary and sufficient conditions for each function of the class $H_p^\omega$ (where $1<p<\infty$, and $\omega$ is a modulus of continuity) to be equivalent to a continuous function on $[0,1]$ or to a function of the class $\operatorname{Lip}\alpha$. Ul'yanov's research for functions of one variable was continued by V. A. Andrienko (RZhMat., 1969, 2B110). In the present paper, analogous questions for functions of several variables are considered.
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