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Matrix Mean Series in Terms of Boundary Orthogonal Systems and Functions in the Classes H∞ and Ep

✍ Scribed by I. Bruj; G. Schmieder

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
124 KB
Volume
118
Category
Article
ISSN
0021-9045

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✦ Synopsis

We give conditions for orthonormal systems on the boundary of a plane Jordan domain which are necessary and sufficient for an arbitrary series in terms of this orthonormal system to be the Fourier series of some function in H 1 ðGÞ resp. E P ðGÞð15p51Þ: Our results contain a classical criterion of Fej! e er for the boundedness of a holomorphic function in the unit disk. # 2002 Elsevier Science (USA)

The following well-known criterion for the boundedness of a function in HðDÞ goes back to Fej! e er [5, p. 22; 6, Chaps. III, IV]:

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The main goal of this paper is to construct Orthogonal Appell systems of polynomial solutions of the Riesz and Moisil-Théodoresco systems in finite cylinders of R 3 . This will be done in the spaces of square integrable functions over R and H. Some important properties of the systems are discussed.