Relations between mixed moduli of smoothness, and embedding theorems for Nikol’skii classes

Author:

Potapov M. K.,Simonov B. V.,Tikhonov S. Yu.

Publisher

Pleiades Publishing Ltd

Subject

Mathematics (miscellaneous)

Reference10 articles.

1. S. M. Nikol’skii, “Functions with Dominant Mixed Derivative Satisfying a Multiple Hölder Condition,” Sib. Mat. Zh. 4(6), 1342–1364 (1963) [Am. Math. Soc. Transl., Ser. 2, 102, 27–51 (1973)].

2. O. V. Besov, V. P. Il’in, and S. M. Nikol’skii, Integral Representations of Functions and Imbedding Theorems (Nauka, Moscow, 1975; J. Wiley & Sons, New York, 1978, 1979).

3. M. K. Potapov, “Imbedding Classes of Functions with Dominant Mixed Modulus of Smoothness,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 131, 199–210 (1974) [Proc. Steklov Inst. Math. 131, 206–218 (1975)].

4. P. L. Ul’yanov, “The Imbedding of Certain Function Classes H p ω ,” Izv. Akad. Nauk SSSR, Ser. Mat. 32(3), 649–686 (1968) [Math. USSR, Izv. 2, 601–637 (1968)].

5. M. K. Potapov, B. V. Simonov, and S. Yu. Tikhonov, “Relations between Moduli of Smoothness in Different Metrics,” Vestn. Mosk. Univ., Ser. 1: Mat., Mekh., No. 3, 17–25 (2009) [Moscow Univ. Math. Bull. 64, 105–112 (2009)].

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