The article considers the Lorentz space $L_{p,\tau}(\mathbb{T}^{m})$, $2\pi$ of periodic functions of many variables and spaces with mixed logarithmic smoothness. Equivalent norms of a space with mixed logarithmic smoothness are found and embedding theorems are proved.
On the exactness of the conditions of embedding theorems for spaces of functions with mixed logarithmic smoothness
On orders of approximation functions of generalized smoothness in Lorentz spaces
On $M$ -- terms approximations Besov classes in Lorentz spaces
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