In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO a...In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.展开更多
Kytmanov and Myslivets gave a special Cauchy principal value of the singular integral on the bounded strictly pseudoconvex domain with smooth boundary. By means of this Cauchy integral principal value, the correspondi...Kytmanov and Myslivets gave a special Cauchy principal value of the singular integral on the bounded strictly pseudoconvex domain with smooth boundary. By means of this Cauchy integral principal value, the corresponding singular integral and a composition formula are obtained. This composition formula is quite different from usual ones in form. As an application, the corresponding singular integral equation and the system of singular integral equations are discussed as well.展开更多
The theory of iterates of holomorphic maps is a very active topic in recent years. The well-known Denjoy-Wolff theorem characterized the asymptotic behavior of the iterate sequences of holomorphic self-maps in the uni...The theory of iterates of holomorphic maps is a very active topic in recent years. The well-known Denjoy-Wolff theorem characterized the asymptotic behavior of the iterate sequences of holomorphic self-maps in the unit disc △C. Subsequent authors extended this theorem to some special domains of C^n(n】1). Briefly speaking, the research展开更多
This paper shows that the 8-problem for holomorphic (0, 2)-forms on Hubert spaces is solv-able on pseudoconvex open subsets. By using this result, the authors investigate the existence of the solution of the -equation...This paper shows that the 8-problem for holomorphic (0, 2)-forms on Hubert spaces is solv-able on pseudoconvex open subsets. By using this result, the authors investigate the existence of the solution of the -equation for holomorphic (0, 2)-forms on pseudoconvex domains in D.F.N. spaces.展开更多
In this article we always assume r+q≤n, otherwise the result is trivial. Now we introduce some definitions and notations.Definition 1. Suppose D is a connected open subset in an n-dimensional complex manifold with C^...In this article we always assume r+q≤n, otherwise the result is trivial. Now we introduce some definitions and notations.Definition 1. Suppose D is a connected open subset in an n-dimensional complex manifold with C^2-boundary. We say function φ is a defining function of if there exists an open neighborhood U of x such that φ: U→R and D ∩ U={y∈M|φ(y)【0},展开更多
A necessary and sufficient condition for the boundedness of the operator: (T s,u,v f)(ξ) =h u+va (ξ)∫ Ω a h s(ξ′)K s,u,v (ξ,ξ′)f(ξ′) d v(ξ′) on L p(Ω a, d v λ),1<p<∞, is obtained, where Ω a=ξ=(...A necessary and sufficient condition for the boundedness of the operator: (T s,u,v f)(ξ) =h u+va (ξ)∫ Ω a h s(ξ′)K s,u,v (ξ,ξ′)f(ξ′) d v(ξ′) on L p(Ω a, d v λ),1<p<∞, is obtained, where Ω a=ξ=(z,w)∈ C n+m : z∈ C n, w∈ C m, |z| 2+|w| 2/a <1, h(ξ)=(1-|z| 2) a-|w| 2 and K x,u,v (ξ,ξ′). This generalizes the works in literature from the unit ball or unit disc to the weakly pseudoconvex domain Ω a. As an application, it is proved that f∈L p H (Ω a, d v λ) implies h |α|a+|β| (ξ)D α 2D β zf∈L p(Ω a, d v λ), 1≤p<∞, for any multi index α=(α 1,...,α n) and β=(β 1,...,β n). An interesting question is whether the converse holds.展开更多
In this paper we obtain non-isotropic weighted Lp estimates with the boundary distance weight function for the-equation on piecewise smooth strictly pseudoconvex domains under a hypoth- esis of complex transversality ...In this paper we obtain non-isotropic weighted Lp estimates with the boundary distance weight function for the-equation on piecewise smooth strictly pseudoconvex domains under a hypoth- esis of complex transversality in Cn using the explicit formula of solutions by Berndtsson-Andersson.展开更多
基金supported by the National Natural Science Foundation of China(12271101)。
文摘In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.
基金the Natural Science Foundation of Zhejiang Province (Y605149)the National Natural Science Foundation of China (10571156)
文摘Kytmanov and Myslivets gave a special Cauchy principal value of the singular integral on the bounded strictly pseudoconvex domain with smooth boundary. By means of this Cauchy integral principal value, the corresponding singular integral and a composition formula are obtained. This composition formula is quite different from usual ones in form. As an application, the corresponding singular integral equation and the system of singular integral equations are discussed as well.
文摘The theory of iterates of holomorphic maps is a very active topic in recent years. The well-known Denjoy-Wolff theorem characterized the asymptotic behavior of the iterate sequences of holomorphic self-maps in the unit disc △C. Subsequent authors extended this theorem to some special domains of C^n(n】1). Briefly speaking, the research
基金The first author was supported by KOSEF postdoctoral fellowship 1998 and the second author was supported by the Brain Korea 21 P
文摘This paper shows that the 8-problem for holomorphic (0, 2)-forms on Hubert spaces is solv-able on pseudoconvex open subsets. By using this result, the authors investigate the existence of the solution of the -equation for holomorphic (0, 2)-forms on pseudoconvex domains in D.F.N. spaces.
基金Project supported by the National Natural Science Foundation of China
文摘In this article we always assume r+q≤n, otherwise the result is trivial. Now we introduce some definitions and notations.Definition 1. Suppose D is a connected open subset in an n-dimensional complex manifold with C^2-boundary. We say function φ is a defining function of if there exists an open neighborhood U of x such that φ: U→R and D ∩ U={y∈M|φ(y)【0},
文摘A necessary and sufficient condition for the boundedness of the operator: (T s,u,v f)(ξ) =h u+va (ξ)∫ Ω a h s(ξ′)K s,u,v (ξ,ξ′)f(ξ′) d v(ξ′) on L p(Ω a, d v λ),1<p<∞, is obtained, where Ω a=ξ=(z,w)∈ C n+m : z∈ C n, w∈ C m, |z| 2+|w| 2/a <1, h(ξ)=(1-|z| 2) a-|w| 2 and K x,u,v (ξ,ξ′). This generalizes the works in literature from the unit ball or unit disc to the weakly pseudoconvex domain Ω a. As an application, it is proved that f∈L p H (Ω a, d v λ) implies h |α|a+|β| (ξ)D α 2D β zf∈L p(Ω a, d v λ), 1≤p<∞, for any multi index α=(α 1,...,α n) and β=(β 1,...,β n). An interesting question is whether the converse holds.
基金supported by the Korea Research Foundation Grant funded by Korea Government(MOEHRD,Basic Research Promotion Fund)(Grant No.KRF-2005-070-C00007)
文摘In this paper we obtain non-isotropic weighted Lp estimates with the boundary distance weight function for the-equation on piecewise smooth strictly pseudoconvex domains under a hypoth- esis of complex transversality in Cn using the explicit formula of solutions by Berndtsson-Andersson.
