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ISSN 1088-6826(e) ISSN 0002-9939(p)

On multipliers for Hardy-Sobolev spaces

Author(s): Frank Beatrous; Jacob Burbea
Journal: Proc. Amer. Math. Soc. 136 (2008), 2125-2133.
MSC (2000): Primary 32A35
Posted: February 21, 2008
MathSciNet review: 2383518
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Abstract | References | Similar articles | Additional information

Abstract: It is shown that membership of holomorphic functions in Hardy-Sobolev spaces in the unit ball cannot be characterized by finiteness of any integral norm. In addition, sufficient conditions are given for a holomorphic function to be a pointwise multiplier of a Hardy-Sobolev space.

References:

1.: W. Arveson, Subalgebras of -algebras III: Multivariable operator theory, Acta Math. 181 (1998), 159-228. MR 1668582 (2000e:47013)
2.: F. Beatrous, Boundary continuity of holomorphic functions in the ball, Proc. Amer. Math. Soc. 97 (1986), 23-29. MR 831380 (87d:32008)
3.: F. Beatrous and J. Burbea, Holomorphic Sobolev spaces on the ball, Dissertationes Math. 256 (1989), 1-57. MR 1010151 (90k:32010)
4.: Z. Chen, Characterizations of Arveson's Hardy space, Complex Variables 48 (2003), 453-465. MR 1974382 (2004c:32010)
5.: W. Rudin, Function Theory in the Unit Ball of $\mathbb{C}^n$ , Springer-Verlag, 1980. MR 601594 (82i:32002)
6.: P. Ryan and M. Stoll, Hardy-Sobolev Spaces and Banach Algebras on the Unit Ball in $\mathbb{C}^n$ , preprint.
7.: J. Ryll and P. Wojtaszczyk, On homogeneous polynomials on a complex ball, Trans. Amer. Math. Soc. 276 (1983), 107-116. MR 684495 (84f:32004)

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Additional Information:

Frank Beatrous
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: beatrous@pitt.edu

Jacob Burbea
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: burbea@pitt.edu

DOI: 10.1090/S0002-9939-08-09187-9
PII: S 0002-9939(08)09187-9
Received by editor(s): January 26, 2007,
Received by editor(s) in revised form: April 2, 2007
Posted: February 21, 2008
Communicated by: Mei-Chi Shaw
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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