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The Growth of Derivatives of Multipliers of Fractional Cauchy Transforms

✍ Scribed by D.J. Hallenbeck; K. Samotij

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 201 KB
Volume: 212
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5548

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✦ Synopsis

In this paper we prove a number of sharp results on the permissible growth of derivatives of multipliers of fractional Cauchy transforms. For example, we prove that if f g M then there exists a positive constant C such that

H M 1 1yr 1qlog 1r 1 y r Ž . Ž . y w . for r g 0, 1 . This result is proved to be sharp.

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