In this paper,we study the integrals and growth properties of the products multiplying types of polynomials and the Poisson kernel in the half space.By gradually weakening the convergence conditions and redefining the...In this paper,we study the integrals and growth properties of the products multiplying types of polynomials and the Poisson kernel in the half space.By gradually weakening the convergence conditions and redefining the measure,two special cases,namely the growth properties of the integrals multiplying two types of harmonic polynomials and the Poisson kernel,are obtained to solve the Dirichlet boundary value problem of the polyharmonic equation.Moreover,we generalize the results concerning the modified Poisson integral in the half space.展开更多
In this article,we consider the integral representation of harmonic functions.Using a property of the modified Poisson kernel in a half plane,we prove that a harmonic function u(z) in a half plane with its positive pa...In this article,we consider the integral representation of harmonic functions.Using a property of the modified Poisson kernel in a half plane,we prove that a harmonic function u(z) in a half plane with its positive part u+(z)=max{u(z),0} satisfying a slowly growing condition can be represented by its integral of a measure on the boundary of the half plan.展开更多
文摘In this paper,we study the integrals and growth properties of the products multiplying types of polynomials and the Poisson kernel in the half space.By gradually weakening the convergence conditions and redefining the measure,two special cases,namely the growth properties of the integrals multiplying two types of harmonic polynomials and the Poisson kernel,are obtained to solve the Dirichlet boundary value problem of the polyharmonic equation.Moreover,we generalize the results concerning the modified Poisson integral in the half space.
基金the National Natural Science Foundation of China(No.10671022)Research Foundation for Doctor Programme (No.20060027023)Henan Institute of Education Youth Scientific Research Fund (No.20070107)
文摘In this article,we consider the integral representation of harmonic functions.Using a property of the modified Poisson kernel in a half plane,we prove that a harmonic function u(z) in a half plane with its positive part u+(z)=max{u(z),0} satisfying a slowly growing condition can be represented by its integral of a measure on the boundary of the half plan.
