Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C^（1） smooth boundary on a Stein manifold. As an a...Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C^（1） smooth boundary on a Stein manifold. As an application the authors discuss the regularization problem for linear singular integral equations with Bochner-Martinelli kernel and variable coefficients; using permutation formula, the singular integral equation can be reduced to a fredholm equation.展开更多
A homotopy formula for a loced q-concave wedge in Stein manifolds is obtained, by using this formula the -equation on local q-concave wedges is solved, and an extension problem on local q-concave wedges is discussed.
By means of the Hermitian metric and Chern connection, Qiu [4] obtained the Koppelman-Leray-Norguet formula for （p, q） differential forms on an open set with C^1 piecewise smooth boundary on a Stein manifold, and un...By means of the Hermitian metric and Chern connection, Qiu [4] obtained the Koppelman-Leray-Norguet formula for （p, q） differential forms on an open set with C^1 piecewise smooth boundary on a Stein manifold, and under suitable conditions gave the solutions of δ^--equation on a Stein manifold. In this article, using the method of Range and Siu [5], under suitable conditions, the authors complicatedly calculate to give the uniform estimates of solutions of δ^--equation for （p, q） differential forms on a Stein manifold.展开更多
Let D be a bounded domain with piecewise C^（1） smooth orientable boundary on Stein manifolds, and let Φ（z） be a Cauchy type integral with Bochner-Martinelli kernel Ω（φ^V, S^-, S） and Holder continuous density...Let D be a bounded domain with piecewise C^（1） smooth orientable boundary on Stein manifolds, and let Φ（z） be a Cauchy type integral with Bochner-Martinelli kernel Ω（φ^V, S^-, S） and Holder continuous density function φ（ζ）, the authors define a solid angular coefficient α（t） at the point t∈δD, prove that there exist the interior and outer limit values Φ^±（t） under the meaning of the Cauchy principal value, and obtain the more general Plemelj formula and jump formula.展开更多
In this paper,we first obtain a unified integral representation on the analytic varieties of the general bounded domain in Stein manifolds(the two types bounded domains in[3]are regarded as its special cases).Secondly...In this paper,we first obtain a unified integral representation on the analytic varieties of the general bounded domain in Stein manifolds(the two types bounded domains in[3]are regarded as its special cases).Secondly we get the integral formulas of the solution of∂-equation.And we use a new and unique method to give a uniform estimate of the solution of∂-equation,which is different from Henkin's method.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)
The homotopy formulas of (r,s) differential forms and the solution of equation of type (r,s) on local q-convex domains in Stein manifolds are obtained.The homotopy formulas on local q-convex domains have important app...The homotopy formulas of (r,s) differential forms and the solution of equation of type (r,s) on local q-convex domains in Stein manifolds are obtained.The homotopy formulas on local q-convex domains have important applications in uniform estimates of equation and holomorphic extension of CR-manifolds.展开更多
A new Koppelman-Leray-Norguet formula of (p,q) differential forms for a strictly pseudoconvex polyhedron with not necessarily smooth boundary on a Stein manifold is obtained, and an integral representation for the sol...A new Koppelman-Leray-Norguet formula of (p,q) differential forms for a strictly pseudoconvex polyhedron with not necessarily smooth boundary on a Stein manifold is obtained, and an integral representation for the solution of -equation on this domain which does not involve integrals on boundary is given, so one can avoid complex estimates of boundary integrals.展开更多
In this paper, by using holomorphic support f unction of strictly pseudoconvex domain on Stein manifolds and the kernel define d by DEMAILY J P and Laurent Thiebaut, we construct two integral operators T q and S q whi...In this paper, by using holomorphic support f unction of strictly pseudoconvex domain on Stein manifolds and the kernel define d by DEMAILY J P and Laurent Thiebaut, we construct two integral operators T q and S q which are both belong to C s+α p,q-1 (D) and ob tain integral representation of the solution of (p,q)-form b-equation on the boundary of pseudoconvex domain in Stein manifolds and the L s p,q extimates for the solution.展开更多
基金The project was supported by the Natural Science Foundation of Fujian Province of China (Z0511002)the National Science Foundation of China (10271097,10571144)+1 种基金Foundation of Tianyuan (10526033)Chen L P, the Corresponding author
文摘Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C^（1） smooth boundary on a Stein manifold. As an application the authors discuss the regularization problem for linear singular integral equations with Bochner-Martinelli kernel and variable coefficients; using permutation formula, the singular integral equation can be reduced to a fredholm equation.
文摘A homotopy formula for a loced q-concave wedge in Stein manifolds is obtained, by using this formula the -equation on local q-concave wedges is solved, and an extension problem on local q-concave wedges is discussed.
基金the National Natural Science Foundation of China(10571144,10771174,10601,040)Program for New Century Excellent Talents in Xiamen University
文摘By means of the Hermitian metric and Chern connection, Qiu [4] obtained the Koppelman-Leray-Norguet formula for （p, q） differential forms on an open set with C^1 piecewise smooth boundary on a Stein manifold, and under suitable conditions gave the solutions of δ^--equation on a Stein manifold. In this article, using the method of Range and Siu [5], under suitable conditions, the authors complicatedly calculate to give the uniform estimates of solutions of δ^--equation for （p, q） differential forms on a Stein manifold.
文摘Let D be a bounded domain with piecewise C^（1） smooth orientable boundary on Stein manifolds, and let Φ（z） be a Cauchy type integral with Bochner-Martinelli kernel Ω（φ^V, S^-, S） and Holder continuous density function φ（ζ）, the authors define a solid angular coefficient α（t） at the point t∈δD, prove that there exist the interior and outer limit values Φ^±（t） under the meaning of the Cauchy principal value, and obtain the more general Plemelj formula and jump formula.
文摘In this paper,we first obtain a unified integral representation on the analytic varieties of the general bounded domain in Stein manifolds(the two types bounded domains in[3]are regarded as its special cases).Secondly we get the integral formulas of the solution of∂-equation.And we use a new and unique method to give a uniform estimate of the solution of∂-equation,which is different from Henkin's method.
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)
基金Project supported by the National Natural Science Foundation of China.
文摘The homotopy formulas of (r,s) differential forms and the solution of equation of type (r,s) on local q-convex domains in Stein manifolds are obtained.The homotopy formulas on local q-convex domains have important applications in uniform estimates of equation and holomorphic extension of CR-manifolds.
基金Supported by the National Natural Science Foundation and Mathematical "Tian Yuan" Foundation of China and the Natural Science Foundation of Fujian (Grant No. 10271097, TY10126033, F0110012)
文摘A new Koppelman-Leray-Norguet formula of (p,q) differential forms for a strictly pseudoconvex polyhedron with not necessarily smooth boundary on a Stein manifold is obtained, and an integral representation for the solution of -equation on this domain which does not involve integrals on boundary is given, so one can avoid complex estimates of boundary integrals.
文摘In this paper, by using holomorphic support f unction of strictly pseudoconvex domain on Stein manifolds and the kernel define d by DEMAILY J P and Laurent Thiebaut, we construct two integral operators T q and S q which are both belong to C s+α p,q-1 (D) and ob tain integral representation of the solution of (p,q)-form b-equation on the boundary of pseudoconvex domain in Stein manifolds and the L s p,q extimates for the solution.
