Moduli of continuity in and
Author:
Z. Ditzian
Journal:
Trans. Amer. Math. Soc. 282 (1984), 611623
MSC:
Primary 26B05; Secondary 41A25, 46E35
MathSciNet review:
732110
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Abstract 
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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.
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 [1]
 Z. Ditzian, Some remarks on approximation theorems on various Banach spaces, J. Math. Anal. Appl. 77 (1980), 567576. 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), 259305. 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, SpringerVerlag, Berlin and New York, 1976, pp. 119140. 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. 341351. 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:
http://dx.doi.org/10.1090/S00029947198407321109
PII:
S 00029947(1984)07321109
Keywords:
Moduli of continuity in smoothness of function spaces,
multivariate semigroups of contractions
Article copyright:
© Copyright 1984
American Mathematical Society
