Kashin, B. S.; Temlyakov, V. N. Estimate of approximate characteristics for classes of functions with bounded mixed derivative. (English. Russian original) Zbl 0878.46023 Math. Notes 58, No. 6, 1340-1342 (1995); translation from Mat. Zametki 58, No. 6, 922-925 (1995). The authors supplement an earlier paper of theirs [Math. Notes 56, No. 5, 1137-1157 (1994; Zbl 0836.41008)] by establishing lower bounds for the \(\varepsilon\)-entropy numbers and Kolmogorov widths of additional classes of spaces of functions of several variables having bounded mixed derivatives. Reviewer: T.Feeman (Villanova) Cited in 9 Documents MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 41A46 Approximation by arbitrary nonlinear expressions; widths and entropy Keywords:entropy number; Kolmogorov width; spaces of functions of several variables having bounded mixed derivatives Citations:Zbl 0836.41008 PDFBibTeX XMLCite \textit{B. S. Kashin} and \textit{V. N. Temlyakov}, Math. Notes 58, No. 6, 1340--1342 (1995; Zbl 0878.46023); translation from Mat. Zametki 58, No. 6, 922--925 (1995) Full Text: DOI References: [1] B. S. Kashin and V. N. Temlyakov,Mat. Zametki [Math. Notes],56, No. 5, 57–86 (1994). [2] É. S. Belinskii, ”Asymptotic characteristics of function classes with restrictions on the mixed derivative (mixed difference),” in:Studies in the Theory of Functions of Several Real Variables [in Russian], Yaroslavl State University, Yaroslavl (1990), pp. 22–37. [3] V. N. Temlyakov,Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],301, No. 2, 288–291 (1988). [4] V. N. Temlyakov, ”Estimates of asymptotic characteristics for classes of functions with bounded mixed derivative or difference,”Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.],189 138–168 (1989). [5] A. Pietsch,Operator Ideals, Deutsch. Verlag Wissensch., Berlin (1978); English transl.: North-Holland, Amsterdam (1980). [6] Din’ Zung,Approximation of Smooth Functions of Several Variables by Means of Harmonic Analysis, D. Sc. Thesis, Moscow State University, Moscow (1985). · Zbl 0605.41033 [7] V. N. Temlyakov,Approximation of Periodic Functions, Nova Science Publishers (1993). · Zbl 0899.41001 [8] V. N. Temlyakov, ”Approximation of functions with bounded mixed derivative,”Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.],178, 1–121, (1986). · Zbl 0668.41024 [9] G. G. Lorentz,Bull. Amer. Math. Soc.,72, 903–937 (1966). · Zbl 0158.13603 [10] G. Pisier,The Volume of Convex Bodies and Banach Space Geometry, Cambridge University Press, Cambridge (1989). · Zbl 0698.46008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.