A class of quadrature formulas and related Marcinkiewicz-Zygmund inequalities(一类求积公式及相关Marcinkiewicz-Zygmund不等式)

In this paper, we establish the Simpson quadrature formula for continuous periodic functions and investigate its quadrature accuracy for trigonometric polynomials, that is, when the quadrature formula holds exactly. Further, the Marcinkiewicz-Zygmund inequalities related to the Simpson formula is investigated with respect to the Lp norm by utilizing tools such as the discrete Fourier operators and the Vallee-Poussin operators.构建了连续周期函数的Simpson求积公式，并探究了其关于三角多项式的求积精度，即求积公式何时精确成立。进一步，在Lp范数下利用离散的Fourier算子和Vallee-Poussin算子等工具，研究了与Simpson求积公式相对应的Marcinkiewicz-Zygmund不等式。