Transactions of the American Mathematical Society

Author(s): Wade C. Ramey; HeungSu Yi
Journal: Trans. Amer. Math. Soc. 348 (1996), 633-660.
MSC (1991): Primary 31B05; Secondary 31B10, 30D55, 30D45
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract: We study harmonic Bergman functions on the upper half-space of $\bold{R}^n$ . Among our main results are: The Bergman projection is bounded for the range $1< p < \infty$ ; certain nonorthogonal projections are bounded for the range $1\leq p < \infty$ ; the dual space of the Bergman $L^1$

-space is the harmonic Bloch space modulo constants; harmonic conjugation is bounded on the Bergman spaces for the range $1\leq p < \infty$ ; the Bergman norm is equivalent to a ``normal derivative norm'' as well as to a ``tangential derivative norm''.

1.: L. Ahlfors, Some remarks on Teichmüller's space of Riemann surfaces, Ann. of Math. 74 (1961), 171--191. MR 34:4480
2.: H. Ajmi and W. Ramey, Harmonic Bloch functions on the upper half space (to appear).
3.: S. Axler, Bergman spaces and their operators, Surveys of Some Recent Results in Operator Theory, Vol. 1, Pitman Research Notes in Math. 171, Pitman, 1988, pp. 1--50. MR 90b:47048
4.: S. Axler, P. Bourdon and W. Ramey, Harmonic function theory, Springer-Verlag, New York, 1992. MR 93f:31001
5.: C. Fefferman and E. Stein, -spaces of several variables, Acta Math. 129 (1972), 137--193. MR 56:6263
6.: F. Forelli and W. Rudin, Projections on spaces of holomorphic functions in balls, Indiana Univ. Math. J. 24 (1974), 593--602. MR 50:10332
7.: G. H. Hardy and J. E. Littlewood, Some properties of conjugate functions, J. Reine Angew. Math. 167 (1931), 405--423
8.: H. S. Shapiro, Global geometric aspects of Cauchy's problem for the Laplace operator, research report TRITA-MAT-1989-37, Royal Inst. Tech., Stockholm.
9.: A. Shields and D. Williams, Bounded projections, duality, and multipliers in spaces of analytic functions, Trans. Amer. Math. Soc. 162 (1971), 287--302. MR 44:790
10.: E. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, NJ, 1970. MR 44:7280
11.: E. Stein and G. Weiss, Fourier analysis on Euclidean spaces, Princeton Univ. Press, Princeton, NJ, 1971. MR 46:4102
12.: K. Zhu, Operator theory in function spaces, Marcel Dekker, New York and Basel, 1990. MR 92c:47031

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 31B05, 31B10, 30D55, 30D45

Wade C. Ramey
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027
Email: ramey@math.msu.edu

HeungSu Yi
Affiliation: Global Analysis Research Center, Department of Mathematics, Seoul National University, Seoul, Korea \#151-742
Email: hsyi@math.snu.ac.kr

DOI: 10.1090/S0002-9947-96-01383-9
PII: S 0002-9947(96)01383-9
Keywords: Bergman kernel, projection operators, dual spaces, harmonic Bloch space
Received by editor(s): October 13, 1994
Copyright of article: Copyright 1996, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6850(e) ISSN 0002-9947(p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2008, American Mathematical Society Privacy Statement		Search the AMS