q-Moduli of Continuity in Hp([formula omitted]), p>0, and an Inequality of Hardy and Littlewood

Some aspects of the interplay between approximation properties of analytic functions and the smoothness of its boundary values are discussed. One main result describes the equivalence of a special q-modulus of continuity and an intrinsic K-functional. Further, a generalization of a theorem due to G....

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Bibliographic Details
Published in:Journal of approximation theory 2002-04, Vol.115 (2), p.238-259
Main Authors: Kryakin, Yuri, Trebels, Walter
Format: Article
Language:English
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Summary:Some aspects of the interplay between approximation properties of analytic functions and the smoothness of its boundary values are discussed. One main result describes the equivalence of a special q-modulus of continuity and an intrinsic K-functional. Further, a generalization of a theorem due to G. H. Hardy and J. E. Littlewood (1932, Math. Z.34, 403–439) on the growth of fractional derivatives is deduced with the help of this K-functional.
ISSN:0021-9045
1096-0430
DOI:10.1006/jath.2001.3656