Remarks on weighted harmonic Bergman functions on half-spaces
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
On the setting of the upper half-space H of the Euclidean n-space, we first estimate the size of partial derivatives of any order for functions in weighted harmonic Bergman spaces and then we show that any partial derivative of weighted harmonic Bergman function behaves nicely on any proper half-space contained in H. Also, we show that if any partial derivative of a given weighted harmonic Bergman function u vanishes on H, then so does u.
Abstract
On the setting of the upper half-space H of the Euclidean n-space, we first estimate the size of partial derivatives of any order for functions in weighted harmonic Bergman spaces and then we show that any partial derivative of weighted harmonic Bergman function behaves nicely on any proper half-space contained in H. Also, we show that if any partial derivative of a given weighted harmonic Bergman function u vanishes on H, then so does u.
참고문헌 (9)
- S. Axler, "Harmonic function theory" (1992), Springer-Verlag
- F. Beatrous, "Behavior of holomorphic functions near weakly pseudoconvex boundary points", Indiana Univ. Math. J., 40(3), pp.915~966 (1991)
- R. R. Coifman, "Representation theorems for holomorphic and harmonic functions in Lp", Asterisque, 77, pp.11~66 (1980)
- H. Hedenmalm, "Theory of Bergman spaces" (2000), Springer-Verlag
- H. Kang, "Estimates of the harmonic Bergman kernel on smooth domains", Journal of Functional Analysis, 185, pp.220~239 (2001)
- 구형운, "Weighted Harmonic Bergman functions on Half-Spaces", 대한수학회지, 42(5), pp.975~1002 (2005), 대한수학회
- H. Koo, "Weighted harmonic Bergman kernel on half-spaces", J. Math. Soc. Japan, 58(2), pp.351~362 (2006)
- W. Ramey, "Harmonic Bergman functions on half-spaces", Trans. Amer. Math. Soc., 348, pp.633~660 (1996)
- K. Zhu, "Operator theory in function spaces" (1990), Marcel Dekker, Inc.