q-超球多项式与若干Rogers-Ramanujan型恒等式

利用ｑ－超球多项式的两个简单性质,建立了关于ｑ－级数的两个变换公式,借助这些变换公式并结合著名的Ｒｏｇｅｒｓ－Ｒａｍａｎｕｊａｎ恒等式,给出了若干Ｒｏｇｅｒｓ－Ｒａｍａｎｕｊａｎ型恒等式的简洁证明。     

q-微分算子的一个恒等式及其应用

应用q-微分算子Leibniz公式，证明了q-微分算子的一个恒等式，并应用此恒等式导出了著名的Sears变换及Al－Salam－Carlitz正交关系等重要结论，还得到了Askey－Roy积分的一个拓广     

波动方程初值问题的解在两类积分中的应用

利用波动方程初值问题解的特点给出了圆域上一类反常二重积分和球面上第一类曲面积分的微分算子级数公式解和定积分公式解.通过举例说明了该方法相对于常规解法的简便实用性.     

积分恒等式及其在无穷级数求和中的应用

借助L2[0,π]中标准正交基展开理论,得到积分恒等式,然后运用这个积分恒等式,通过定积分计算给出几个无穷级数和公式的简单证明,同时得到一些新的无穷级数和公式.     

关于几类积分的微分算子级数解法

利用微分算子级数法 ,将若干类广义积分及变上限函数的积分问题化为微分运算 ,介绍它们转换的条件、公式及实例 .     

一类q-级数恒等式的新证法

本文利用一个已知的变换公式及其它基本超几何函数的求和公式，给出了一类ｑ级数恒等式的新的更简单的证明，并建立了该类恒等式的一般形式．     

SCP-Fourier级数的系数

本文利用Ｐ．Ｓ．Ｂｕｌｌｅｎ和Ｓ．Ｎ．Ｍｕｋａｏｐａｄｈｙａｙ在［１］中建立了ＳＣＰ—积分的分部积分公式给出了ＳＣＰ－Ｆｏｕｒｉｅｒ级数的概念，并讨论了ＳＣＰ－Ｆｏｕｒｉｅｒ级数的系数问题。     

实Clifford分析中六类拟Bochner-Martinelli型高阶奇异积分的几个问题

本文借助于Ｈａｄａｍａｒｄ关于高阶奇异积分有限部分的思想,研究关于实 Ｃｌｉｆｆｏｒｄ分析中六个类型(含一个奇点或二个奇点的)拟Ｂｏｃｈｎｅｒ－Ｍａｒｔｉｎｅｌｌｉ型高阶奇异积分的归纳定义、Ｈａｄａｍａｒｄ主值的存在性、递推公式、计算公式、微分公式、Ｐｏｉｎｃａｒｅ－Ｂｅｒｔｒａｎｄ置换公式以及拟Ｂ－Ｍ型高阶奇异积分的Ｈｏｌｄｅｒ连续性等问题．这些问题是研究单、多元复分析的学者们在研究奇异积分时,通常要涉及到的几个问题．     

q超几何级数2Φ0[a,b;z]两个基本恒等式及其一些应用

本文由有限域上交错矩阵方程Ｘ Ｋ２ｖＸ’＝０的解数公式得到ｑ超几何级数２Φ０的一个基本恒等式，并且用它能直接把一些特殊矩阵的这类方程的解数由函数２Φ０表出。另外还用２Φ０的一个恒等式得出Ｆｑ上ｍ阶特殊矩阵的个数。     

q超几何级数_2Φ_0[a,b;z]的两个基本恒等式及其一些应用

本文由有限域上交错矩阵方程ＸＫ２υＸ′＝０的解数公式得到ｑ超几何级数２Φ０的一个基本恒等式，并且用它能直接把一些特殊矩阵的这类方程的解数由函数２Φ０表出．另外还用２Φ０的一个恒等式得出Ｆｑ上ｍ阶特殊矩阵的个数．     

Two operator identities and their applications to terminating basic hypergeometric series and q-integrals

In this paper, we first give two interesting operator identities, and then, using them and the q-exponential operator technique to some terminating summation formulas of basic hypergeometric series and q-integrals, we obtain some q-series identities and q-integrals involving ₃?₂.     

Lp[0,1]空间中弱奇异积分算子性质的研究

首先讨论具有弱奇异核k(s,t)=g(s,t)/│s-t│α的积分算子当0＜α＜1/q(1/p+1/q=1)时在Lp[0,1]上是紧的,进一步得到对于任一给定的q当α＜1/q时,有α阶弱奇异积分算子K*(K的共轭算子)在Lq[0,1]中是紧算子.     

WEIGHTED Lp BOUNDEDNESS FOR MULTILINEAR FRACTIONAL INTEGRAL ON PRODUCT SPACES

For 0 < α < mn and nonnegativeintegers n ≥ 2,m ≥ 1, the multilinear fractional integral is defined by Iα(m )(→f )(x) = ∫(Rn)m 1/ ︱→y |mn-α m ∏ i=1 fi(x-yi)d→y , where →y = (y1,y2,··· ,ym) and →f denotes the m-tuple (f1, f2,··· , fm). In this note, the one-weighted and two-weighted boundednesson Lp(Rn) space for multilinear fractional integral operator Iα(m )and the fractional multi-sublinear maximal operator Mα(m )are established re-spectively. The authors also obtain two-weighted weak type estimate for the...     

A note on generalized q-difference equations for q-beta and Andrews–Askey integral

Two q-difference equations with solutions expressed by q-exponential operator identities are investigated. As applications, two extensions of Ramanujan?s formulas for q-beta integral are given, two generalizations of Andrews–Askey integral are obtained. In addition, generating functions for generalized Al-Salam–Carlitz polynomials are deduced. At last, a generalized transformation identity is gained.     

A q-summation formula,the continuous q-Hahn polynomials and the big q-Jacobi polynomials

Using a general q-summation formula, we derive a generating function for the q-Hahn polynomials, which is used to give a complete proof of the orthogonality relation for the continuous q-Hahn polynomials. A new proof of the orthogonality relation for the big q-Jacobi polynomials is also given. A simple evaluation of the Nassrallah–Rahman integral is derived by using this summation formula. A new q-beta integral formula is established, which includes the Nassrallah–Rahman integral as a special case. The q-summation formula also allows us to recover several strange q-series identities.     

Bressoud polynomials,Rogers–Ramanujan type identities,and applications

In his paper providing an easy proof of the Rogers–Ramanujan identities, D. Bressoud extended his work to multiple series identities. Intrinsic in his works are polynomials with diverse applications to several aspects of \(q\)-series. This paper provides an initial exploration of these polynomials.     

The derivative operator and harmonic number identities

By applying the derivative operator to the corresponding hypergeometric form of a q-series transformation due to Andrews (see Theorem 4 in Theory and Application for Basic Hypergeometric Functions, pp. 191–224, Academic Press, New York, 1975), we establish a general harmonic number identity. As the special cases of it, several interesting Chu–Donno-type identities and Paule–Schneider-type identities are displayed.     

多线性奇异积分算子的加权Lipschitz估计

该文讨论了一类多线性积分算子的加权Lipschitz有界性,通过将多线性积分算子用相应的分数次积分估计，得到一种简明的证明方法.      

An Expansion Formula for q-Series and Applications

In this paper the author proves a q-expansion formula which utilizes the Leibniz formula for the q-differential operator. This expansion leads to new proofs of the Rogers–Fine identity, the nonterminating ₆₅ summation formula, and Watson's q-analog of Whipple's theorem. Andrews' identities for sums of three squares and sums of three triangular numbers are also derived. Other identities of Andrews and new identities for Hecke type series are also discussed.