Composition operators on the Privalov spaces of the unit ball of $\Bbb{C}^n$
0
조회
0
다운로드
0
인용
0
참고문헌
초록
Abstract
Let B and S be the unit ball and the unit sphere in Cn, respectively. Let ¾ be the normalized Lebesgue measure on S. De¯ne the Privalov spaces Np(B) (1 < p < 1) by Np(B) = ½f 2 H(B) : sup 0<r<1 ZSflog(1 + jf(r³)j)gpd¾(³) < 1¾; where H(B) is the space of all holomorphic functions in B. Let ' be a holomorphic self-map of B. Let ¹ denote the pull-back measure ¾ ± ('¤)¡1. In this paper, we prove that the composition operator C' is metrically bounded on Np(B) if and only if ¹(S(³; ±)) · C±n for some constant C and C' is metrically compact on Np(B) if and only if ¹(S(³; ±)) = o(±n) as ± # 0 uniformly in ³ 2 S. Our results are an analogous results for MacCluer's Carleson-measure criterion for the boundedness or compactness of C' on the Hardy spaces Hp(B).
참고문헌 (11)
- "Composition operators on some F-algebras of holo-morphic functions", 7, pp.29~39 (1996)
- "Composition operators between Nevanlinna-type spaces", 257, pp.378~402 (2001)
- "Spectra of compact composition operators onHp", pp.87~103 (1984)
- "Compact composition operators on Hp", pp.237~248 (1985)
- "Angular derivatives and compact compositionoperators on the Hardy and Bergman spaces", 38, pp.878~906 (1986)
- "Isometries of weighted Bergman-Privalov spaces on theunit ball ofCn", 54, pp.341~347 (2002)
- "Hormander's Carleson theorem for the ball", 26, pp.13~17 (1985)
- "Function Theory on the Unit Ball ofCn" (1980), Springer-Verlag
- "Mean growth and Taylor coecients of some topological algebras ofanalytic functions", 35, pp.139~158 (1977)
- "Functional properties of Privalov spaces of holomorphic functions in several variables", 65, pp.230~237 (1999)
- "Compact composition operators on the Area-Nevanlinna class", 17, pp.255~264 (1999)