第Ⅲ类非自共轭锥上的Gamma函数

本文将Ｇａｍｍａ函数及Ｓｉｅｇｅｌ积分推广到一般的第Ⅲ类非自共轭锥上,作为其应用,显式给出了以这些锥为底的管状域（也称第一类Ｓｉｅｇｅｌ域）的Ｃａｕｃｈｙ－Ｓｚｅｇｏ核和形式Ｐｏｉｓｓｏｎ核。关键词     

第Ⅰ类非自共轭锥上的Gamma函数

本文将Ｇａｍｍａ函数及Ｓｉｅｇｅｌ积分推广到一般的第Ⅰ类非自共轭锥上。作为其应用，显式给出了以这些锥为底的管状域（或第一类Ｓｉｅｇｅｌ域）的Ｃａｕｃｈｙ－Ｓｘｅｇｏｅ核和形式Ｐｏｉｓｓｏｎ核。     

第Ⅱ类非自共轭锥上的Gamma函数

本文将Ｇａｍｍａ函数及Ｓｉｅｇｅｌ积分推广到一般的第Ⅱ类非自共轭锥上,作为其应用,显示给出了以这些锥为底的管状域的Ｃａｕｃｈｙ－Ｓｚｅｇｏｅ核和形式Ｐｏｉｓｓｏｎ核。     

第III类非自共轭锥上的Gamma函数

本文将Gamma函数及Siegel积分推广到一般的第III类非自共轭锥上.作为其应用,显式给出了以这些锥为底的管状域(也称第一类Siegel域)的Cauchy-Szeg"o核和形式Poisson核.     

第四类超Cartan域的Bergman核函数

显式给出了第四类超Cartan域的Bergman核函数及其全纯自同构群．     

积域上粗糙核Marcinkiewicz积分的L~p有界性

本文证明了积域上的Ｍａｒｃｉｎｋｉｅｗｉｃｚ积分算子μΩ是Ｌｐ（ＲｎｘＲｍ）（１＜ｐ＜∞）有界的．这里核函数Ω仅满足尺寸条件．即Ω∈Ｌｐ（Ｓｎ－１×Ｓｍ－１）（ｑ＞１）,而不需添加任何光滑性条件．本文结果可视为 Ｓｔｅｉｎ结果的一个改进．     

SiegelE.G函数值的数论性质

本文介绍了ＳｉｅｇｅｌＥ．Ｇ函数值数论性的主要内容，进展和有关的问题。     

某些周期卷积类上的最佳单边逼近

设Ｋ满足性质Ｂ（或Ｋ是ＮＣＶＤ核），本文得到了以Ｋ为核的卷积类Ｂ＿ｐ（或Ｋ＿ｐ），１≤ｐ≤∞，在Ｌ＿１尺度下，借助于三角多项式和周期样条的单边逼近的精确值．ｈ，ｆ⊥Ｓ，则ｈ⊥Ｓ，结合（４．７）我们易知Ｆ∈Ｓ￣－（Ｇ￣＊），且Ｆ⊥Ｓ，Ｆ（０）＝０．由引理６得由引理７得进一步地根据定理２，我们可得（４．６）及（４．８）得另一方面．根据［２］（定理１．７．５）及引理８得由（４．８）、（４．１０）定理得证．作者感谢导师孙永生教授的悉心指导．参考文献     

广义例外华罗庚域的Bergman核函数

计算出两类广义例外华罗庚域的Bergman核函数的显式表达式. 同时利用Appell的多变量的超几何函数给出了例外华罗庚域的Bergman核函数在边界点附近的渐近性质.     

第一类超Cartan域的Bergman核函数 *

显式给出了第一类超Cartan域的Bergman核函数及其全纯自同构群     

Gamma Functions and Siegel Integrals on Nonselfdual Cones

Ｉｎｔｈｅｐａｐｅｒ［１］,ＹｉｎＷｅｉｐｉｎｇｉｎ１９８１ｏｂｔａｉｎｅｄＧａｍｍａｆｕｎｃｔｉｏｎｓａｎｄＳｉｅｇｅｌｉｎｔｅｇｒａｌｓｏｎｎｏｎｓｅｌｆｄｕａｌｃｏｎｅｓＶＩＩｍ１,…,ｍｓ１,ｓａｎｄＶＩＩｍ１,…,ｍｓ１,ｓ,　　Ｉｎｔｈｉｓｐａｐｅｒ,ｗｅｗｉｌｌｄｅｆｉｎｅＧａｍｍａｆｕｎｃｔｉｏｎｓａｎｄＳｉｅｇｅｌｉｎｔｅｇｒａｌｓｏｎｎｏｎｓｅｌｆｄｕａｌｃｏｎｅｓＶＩＩｍ１,…,ｍｓ１３,ｓａｎｄＶＩＩｍ１,…,ｍｓ１３,ｓ．ＴｈｅｎｏｂｔａｉｎＣａｕｃｈｙ－Ｓｚｅｇｏ…     

第三类超Cartan域的Bergman核函数

显式给出了第三类超Cartan域的Bergman核函数及其全纯自同构群。     

第四类华罗庚域的Bergman核函数

本文给出了第四类华罗庚域H EIV上的Bergman核函数,全纯自同构群以 及semi—Reinhardt域上的完备标准正交函数系.     

LINEAR SINGULAR INTEGRAL EQUATION ON DOMAINS COMPOSED BY BALLS

For domains composed by balls in Cn, this paper studies the boundary behaviour of Cauchy type integrals with discrete holomorphic kernels and the corresponding linear singular integral equation on each piece of smooth lower dimensional edges on the boundary of the domain.     

Berezin Transform for Solvable Groups

We study the Berezin transform in the context of solvable groups AN (acting on homogeneous cones and Siegel domains) and determine its spectral decomposition, using an explicit integral kernel representation for the associated eigen-operators in terms of multivariable hypergeometric functions.     

Linear dependence among Siegel modular forms

Theorems are given which describe when high enough vanishing at the cusps implies that a Siegel modular cusp form is zero. Formerly impractical computations become practical and examples are given in degree four. Vanishing order is described by kernels, a type of polyhedral convex hull. Received: November 19, 1998 / Revised: July 5, 1999 / Published online: September 5, 2000     

Hilbert integrals on Siegel domains of type II

The Šilov boundary of a Siegel domain of type II is equivalent to a 2-step nilpotent Lie group. In this paper, we mainly study the L^p-boundness of the Hilbert integrals on Siegel domains of type II by using F. Ricci and E.M. Stein's result about singular integrals on Lie groups^[1]. This is the generalization of part of the work done by P.H.Phong and E.M.Stein in [2]     

ROUGH MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION ON PRODUCT DOMAINS

In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions on kernels. The main results essentially improve and extend some known results.