Moduli of continuity in and

Author:
Z. Ditzian

Journal:
Trans. Amer. Math. Soc. **282** (1984), 611-623

MSC:
Primary 26B05; Secondary 41A25, 46E35

DOI:
https://doi.org/10.1090/S0002-9947-1984-0732110-9

MathSciNet review:
732110

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Abstract | References | Similar Articles | Additional Information

Abstract: The modulus of continuity for is expressed in terms of moduli of continuity in independent directions. Generalizations to other spaces of functions on or are also given.

**[1]**Z. Ditzian,*Some remarks on approximation theorems on various Banach spaces*, J. Math. Anal. Appl.**77**(1980), no. 2, 567–576. MR**593235**, https://doi.org/10.1016/0022-247X(80)90248-6**[2]**V. P. Il′in,*Conditions of validity of inequalities between 𝐿_{𝑝}-norms of partial derivatives of functions of several variables*, Trudy Mat. Inst. Steklov. 96 (1968), 205–242 (Russian); translated in Proc. Steklov Inst. Math., No. 96 (1968): Automat. Programming, Numer. Methods and Functional Anal., Amer. Math. Soc., Providence, R.I., 1968, pp. 259–305. MR**0271724****[3]**H. Johnen and K. Scherer,*On the equivalence of the 𝐾-functional and moduli of continuity and some applications*, Constructive theory of functions of several variables (Proc. Conf., Math. Res. Inst., Oberwolfach, 1976) Springer, Berlin, 1977, pp. 119–140. Lecture Notes in Math., Vol. 571. MR**0487423****[4]**Robert C. Sharpley,*Cone conditions and the modulus of continuity*, Second Edmonton conference on approximation theory (Edmonton, Alta., 1982) CMS Conf. Proc., vol. 3, Amer. Math. Soc., Providence, RI, 1983, pp. 341–351. MR**729339****[5]**Elias M. Stein,*Singular integrals and differentiability properties of functions*, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR**0290095****[6]**A. F. Timan,*Theory of approximation of functions of a real variable*, Translated from the Russian by J. Berry. English translation edited and editorial preface by J. Cossar. International Series of Monographs in Pure and Applied Mathematics, Vol. 34, A Pergamon Press Book. The Macmillan Co., New York, 1963. MR**0192238**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0732110-9

Keywords:
Moduli of continuity in smoothness of function spaces,
multivariate semigroups of contractions

Article copyright:
© Copyright 1984
American Mathematical Society