WEIGHTED HARMONIC BERGMAN FUNCTIONS ON HALF-SPACES

Title & Authors
WEIGHTED HARMONIC BERGMAN FUNCTIONS ON HALF-SPACES
Koo, HYUNGWOON; NAM, KYESOOK; YI, HEUNGSU;

Abstract
On the setting of the upper half-space H of the Eu­clidean n-space, we show the boundedness of weighted Bergman projection for 1 < p < $\small{\infty}$ and nonorthogonal projections for 1 $\small{\leq}$ p < $\small{\infty}$ . Using these results, we show that Bergman norm is equiva­ lent to the normal derivative norms on weighted harmonic Bergman spaces. Finally, we find the dual of b$\small{\_{}$$\small{^{1}}$.
Keywords
weighted Bergman kernel;harmonic Bergman functions;fractional derivative;upper half-space;
Language
English
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References
1.
S. Axler, P. Bourdon, and W. Ramey, Harmonic function theory, Springer-Verlag, New York, 1992

2.
F. Beatrous, Behavior of holomorphic functions near weakly pseudoconvex boundary points, Indiana Univ. Math. J. 40 (1991), no. 3, 915-966

3.
B. R. Choe, Projections, the weighted Bergman spaces, and the Bloch space, Proc. Amer. Math. Soc. 108 (1990), 127-136

4.
B. R. Choe, H. Koo, and H. Yi, Bergman norm estimates of Poisson integrals, Nagoya Math. J. 161 (2001), 85-125

5.
B. R. Choe, H. Koo, and H. Yi, Moment vanishing properties of harmonic Bergman functions, preprint

6.
R. R. Coifman and R. Rochberg, Representation theorems for holomorphic and harmonic functions in $L^P$, Asterisque 77 (1980), 11-66

7.
H. Kang and H. Koo, Estimates of the harmonic Bergman kernel on smooth domains, J. Funct. Anal. 185 (2001), 220-239

8.
H. Koo, K. Nam, and H. Yi, Weighted harmonic Bergman kernel on Half-spaces, to appear J. Math. Soc. Japan

9.
H. Hedenmalm, B. Korenblum, and K. Zhu, Theory of Bergman spaces, Springer-Verlag, New York, 2000

10.
W. Ramey and H. Yi, Harmonic Bergman functions on half-spaces, Trans. Amer. Math. Soc. 348 (1996), 633-660