q-Moduli of Continuity in Hp(D), p>0, and an Inequality of Hardy and Littlewood

✍ Scribed by Yuri Kryakin; Walter Trebels

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 172 KB
• Volume: 115
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.2001.3656

✦ Synopsis

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.