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), 567-576. MR**593235 (81k:41010)****[2]**V. P. Ilin,*Conditions of validity of inequalities between**norms of partial derivatives of functions of several variables*, Proc. Steklov Inst. Math.**96**(1968), 259-305. MR**0271724 (42:6605)****[3]**H. Johnen and K. Scherer,*On equivalence of**functional and moduli of continuity and some applications*, Constructive Theory of Functions of Several Variables (Proc. Conf. Oberwolfbach, 1976), Lecture Notes in Math., vol. 571, Springer-Verlag, Berlin and New York, 1976, pp. 119-140. MR**0487423 (58:7060)****[4]**R. C. Sharpley,*Cone conditions and the modulus of continuity*(Proc. 2nd Edmonton Conf. on Approximation Theory), CMS Conference Proceedings, vol. 3, Amer. Math. Soc., Providence, R. I., 1983, pp. 341-351. MR**729339 (85h:41037)****[5]**E. Stein,*Singular integrals and differentiability properties of functions*, Princeton Univ. Press, Princeton, N. J., 1970. MR**0290095 (44:7280)****[6]**A. F. Timan,*Theory of approximation of functions of a real variable*(English transl.), Pergamon Press, Macmillan, New York, 1963. MR**0192238 (33:465)**

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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