On multipliers for Hardy-Sobolev spaces

Beatrous, Frank; Burbea, Jacob

doi:10.1090/S0002-9939-08-09187-9

On multipliers for Hardy-Sobolev spaces
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by Frank Beatrous and Jacob Burbea PDF

Proc. Amer. Math. Soc. 136 (2008), 2125-2133 Request permission

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

William Arveson, Subalgebras of $C^*$-algebras. III. Multivariable operator theory, Acta Math. 181 (1998), no. 2, 159–228. MR 1668582, DOI 10.1007/BF02392585
Frank Beatrous, Boundary continuity of holomorphic functions in the ball, Proc. Amer. Math. Soc. 97 (1986), no. 1, 23–29. MR 831380, DOI 10.1090/S0002-9939-1986-0831380-3
Frank Beatrous and Jacob Burbea, Holomorphic Sobolev spaces on the ball, Dissertationes Math. (Rozprawy Mat.) 276 (1989), 60. MR 1010151
Zeqian Chen, Characterizations of Arveson’s Hardy space, Complex Var. Theory Appl. 48 (2003), no. 5, 453–465. MR 1974382, DOI 10.1080/0278107031000103421
Walter Rudin, Function theory in the unit ball of $\textbf {C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594, DOI 10.1007/978-1-4613-8098-6
P. Ryan and M. Stoll, Hardy-Sobolev Spaces and Banach Algebras on the Unit Ball in $\mathbb {C}^n$, preprint.
J. Ryll and P. Wojtaszczyk, On homogeneous polynomials on a complex ball, Trans. Amer. Math. Soc. 276 (1983), no. 1, 107–116. MR 684495, DOI 10.1090/S0002-9947-1983-0684495-9