Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the Carleson measure characterization of BMOA functions on the unit ball

Author: Miroljub Jevtić
Journal: Proc. Amer. Math. Soc. 114 (1992), 379-386
MSC: Primary 32A37; Secondary 47B35
MathSciNet review: 1072341
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An equivalent form of the well-known Carleson measure condition that characterizes BMOA functions on the unit ball is given. As an application, it is proved that the Toeplitz operator $ {T_{\bar \varphi }},\varphi \in {H^\infty }(S)$, is bounded on the Hardy-Sobolev space $ H_\alpha ^1,0 < \alpha < \infty $.

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

  • [1] A. Baernstein II, Analytic functions of bounded mean oscillation, Aspects of Contemporary Complex Analysis, Academic Press, New York, 1980, pp. 3-36. MR 623463 (84g:42021)
  • [2] F. Beatrous and J. Burbea, Characterization of spaces of holomorphic functions in the ball, Kodai Math. J. 8 (1985), 36-51. MR 776705 (86j:32007)
  • [3] -, Sobolev spaces of holomorphic functions in the ball, Pitman Research Notes, vol. 227, Pitman, London.
  • [4] R. Coifman, R. Rochberg, and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (1976), 611-635. MR 0412721 (54:843)
  • [5] C. Fefferman and E. Stein, $ {H^p}$ spaces of several variables, Acta Math. 129 (1972), 137-193. MR 0447953 (56:6263)
  • [6] D. Luecking, Forward and reverse Carleson inequalities for functions in Bergman spaces and their derivatives, Amer. J. Math. 107 (1985), 85-111. MR 778090 (86g:30002)
  • [7] L. Hörmander, $ {L^p}$-estimates for (pluri-)-subharmonic functions, Math. Scand. 20 (1976), 65-78.
  • [8] M. Jevtić, Two Carleson measure theorems for Hardy spaces, Proc. of the Koniklijke Nederlandse Akademie van Wetenschappen Ser. A, vol. 92, 1989, pp. 315-321. MR 1020025 (91b:42041)
  • [9] W. Rudin, Function theory in the unit ball of $ {C^N}$, Springer-Verlag, New York, 1980. MR 601594 (82i:32002)
  • [10] F. Shamoyan, The Toeplitz operators on some spaces of analytic functions and a new characterization of the classes BMO, Izv. Akad. Nauk Armyan. SSR Ser. Mat. 22 (1987), 122-132. MR 898512 (88h:47033)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32A37, 47B35

Retrieve articles in all journals with MSC: 32A37, 47B35

Additional Information

Keywords: Carleson measures, BMOA spaces, Toeplitz operators, Hardy-Sobolev spaces
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society