关于Stieltjes系数的不等式及阶的估计

The Fundamental Theorem of Calculus and the HardyLittlewood Maximal Function

本文得出黎曼ζ函数在０＜｜ｓ－１｜＜＋∞的Ｌａｕｒｅｎｔ展式系数，即Ｓｔｉｅｌｔｊｅｓ系数γｎ的不等式及阶的估计式：ｉ）－ｎｅｎ＋（ｌｎ２）ｎ２－（ｌｎ２）ｎ＋１ｎ＋１＜γｎ＜ｎｅｎ－（ｌｎ２）ｎ＋１ｎ＋１（ｎ≥１）ｉ）γｎ＝Ｏｎｎｅｎ＝Ｏｎ！

The fundamental theorem of calculus is a important theorem in the mathematical analysis. The HardyLittlewood maximal function is a very important operator in modern harmnic analysis. We established some weighted generalizations of the fundamental theorem of calculus with the maximal operator.