Nehari and Nevanlinna-Pick Problems and Holomorphic Extensions in the Polydisk in Terms of Restricted BMO

✍ Scribed by M. Cotlar; C. Sadosky

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 250 KB
• Volume: 124
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1994.1105

✦ Synopsis

A new class BMOr is introduced, motivated by the following extension of the Nehari theorem to (d \geqslant 1) : The norm of a bounded (big) Hankel form (B) in the (d)-dimensional torus satisfies (|\phi| \leqslant|B| \leqslant \sqrt{d}|\phi|) where the norm of (\phi), the antianalytic symbol of (B), is taken in BMOr. This extension in turn provides solutions to Nevanlinna-Pick type interpolation problems in the polydisk, with control of the BMOr norm. Necessary and sufficient conditions for the existence of (H^{2} \cap) BMOr extensions of analytic functions defined on a zero variety (V) are given, with control of the norm, under general conditions on (V). C 1994 Academic Press, Inc.