Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Boundary behavior of $ {\rm BMO}(B\sb n)$

Author: Paula A. Russo
Journal: Trans. Amer. Math. Soc. 292 (1985), 733-740
MSC: Primary 32E35; Secondary 32A40
MathSciNet review: 808751
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: If $ f$ is a holomorphic function of bounded mean oscillation in the unit ball of $ {{\mathbf{C}}^n}$, then it has radial limits at almost every point of the boundary of the ball. The question remains as to how nicely one can expect this function to behave on subsets of the boundary of zero measure. For example, there is a holomorphic BMO function in the ball that has a finite radial limit at no point of the $ n$-torus. We show here that this is not an isolated phenomenon; there exists at least one other $ n$-dimensional submanifold of the boundary of the ball with this same behavior.

References [Enhancements On Off] (What's this?)

  • [1] P. Ahern, On the behavior near a torus of functions holomorphic in the ball, Pacific J. Math. 107 (1983), 267-278. MR 705748 (84i:32023)
  • [2] R. R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. (2) 103 (1976), 611-635. MR 0412721 (54:843)
  • [3] H. Federer, Curvature measures, Trans. Amer. Math. Soc. 93 (1959), 418-491. MR 0110078 (22:961)
  • [4] A. Nagel and W. Rudin, Local boundary behavior of bounded holomorphic functions, Canad. J. Math. 30 (1978), 583-592. MR 0486595 (58:6315)
  • [5] C. Pommerenke, On Bloch functions, J. London Math. Soc. 2 (1970), 689-695. MR 0284574 (44:1799)
  • [6] W. Rudin, Function theory in the unit ball of $ {{\mathbf{C}}^n}$, Springer-Verlag, New York and Berlin, 1980. MR 601594 (82i:32002)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 32E35, 32A40

Retrieve articles in all journals with MSC: 32E35, 32A40

Additional Information

Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society