Multidimensional piecewise polynomial approximation on classes of functions with a dominant mixed derivative

In this paper is presented an $n$-parameter method of approximation, by piecewise polynomial functions, on classes $H_p^r$ of functions with a dominant mixed derivative. The method can be used to obtain a best possible estimate in the “power scale” of the $\varepsilon$-entropy of the class $H_p^r$ in the space $L_q$.
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