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
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
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 authors consider proper holomorphic mappings between smoothly bounded pseudoconvex regions in complex 2-space,where the domain is of finite type and admits a transverse circle action.The main result is that the cl...The authors consider proper holomorphic mappings between smoothly bounded pseudoconvex regions in complex 2-space,where the domain is of finite type and admits a transverse circle action.The main result is that the closure of each irreducible component of the branch locus of such a map intersects the boundary of the domain in the union of finitely many orbits of the group action.展开更多
The purpose of this paper is threefold.(i) To explain the effective Kohn algorithm for multipliers in the complex Neumann problem and its difference with the full-real-radical Kohn algorithm, especially in the context...The purpose of this paper is threefold.(i) To explain the effective Kohn algorithm for multipliers in the complex Neumann problem and its difference with the full-real-radical Kohn algorithm, especially in the context of an example of Catlin-D'Angelo concerning the ineffectiveness of the latter.(ii) To extend the techniques of multiplier ideal sheaves for the complex Neumann problem to general systems of partial differential equations.(iii) To present a new procedure of generation of multipliers in the complex Neumann problem as a special case of the multiplier ideal sheaves techniques for general systems of partial differential equations.展开更多
The purpose of this paper is to complement the results by Lanzani and Stein(2017) by showing the dense definability of the Cauchy-Leray transform for the domains that give the counter-examples of Lanzani and Stein(201...The purpose of this paper is to complement the results by Lanzani and Stein(2017) by showing the dense definability of the Cauchy-Leray transform for the domains that give the counter-examples of Lanzani and Stein(2017), where L^p-boundedness is shown to fail when either the "near" C^2 boundary regularity, or the strong C-linear convexity assumption is dropped.展开更多
A new technique of integral representations in Cn, which is different from the well-known Henkin technique, is given. By means of this new technique, a new integral formula for smooth functions and a new integral repr...A new technique of integral representations in Cn, which is different from the well-known Henkin technique, is given. By means of this new technique, a new integral formula for smooth functions and a new integral representation of solutions of the -equations on strictly pseudoconvex domains in Cn are obtained. These new formulas are simpler than the classical ones, especially the solutions of the -equations admit simple uniform estimates. Moreover, this new technique can be further applied to arbitrary bounded domains in Cn so that all corresponding formulas are simplified.展开更多
G. M. Khenkin obtained the solution of (p, q)-form ■_b-equation of strictly pseudoconvex complex manifolds. In this note, we study the solution of (p, q)
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 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 authors consider proper holomorphic mappings between smoothly bounded pseudoconvex regions in complex 2-space,where the domain is of finite type and admits a transverse circle action.The main result is that the closure of each irreducible component of the branch locus of such a map intersects the boundary of the domain in the union of finitely many orbits of the group action.
文摘The purpose of this paper is threefold.(i) To explain the effective Kohn algorithm for multipliers in the complex Neumann problem and its difference with the full-real-radical Kohn algorithm, especially in the context of an example of Catlin-D'Angelo concerning the ineffectiveness of the latter.(ii) To extend the techniques of multiplier ideal sheaves for the complex Neumann problem to general systems of partial differential equations.(iii) To present a new procedure of generation of multipliers in the complex Neumann problem as a special case of the multiplier ideal sheaves techniques for general systems of partial differential equations.
基金supported by the National Science Foundation of USA (Grant Nos. DMS1503612 (Lanzani) and DMS-1265524 (Stein))
文摘The purpose of this paper is to complement the results by Lanzani and Stein(2017) by showing the dense definability of the Cauchy-Leray transform for the domains that give the counter-examples of Lanzani and Stein(2017), where L^p-boundedness is shown to fail when either the "near" C^2 boundary regularity, or the strong C-linear convexity assumption is dropped.
基金the National Natural Science Foundation of China(Grant No.19771068).
文摘A new technique of integral representations in Cn, which is different from the well-known Henkin technique, is given. By means of this new technique, a new integral formula for smooth functions and a new integral representation of solutions of the -equations on strictly pseudoconvex domains in Cn are obtained. These new formulas are simpler than the classical ones, especially the solutions of the -equations admit simple uniform estimates. Moreover, this new technique can be further applied to arbitrary bounded domains in Cn so that all corresponding formulas are simplified.
基金Project supported by the National Natural Science Foundation of China
文摘G. M. Khenkin obtained the solution of (p, q)-form ■_b-equation of strictly pseudoconvex complex manifolds. In this note, we study the solution of (p, q)
