广义Laplace-Stieltjes变换的(p,q)级

The (p,q) order of generalized Laplace-Stieltjes transforms

研究了定义在右半平面的一条从原点出发的Jordan曲线上的广义Laplace-Stieltjes变换所表示的整函数F(s)的增长性.首先定义F(s)在圆周|z|=r上的最大模M(r,F)和最大项m(r,F);其次介绍由最大模所表示的(p,q)级;最后经过研究发现了由最大模所表示的(p,q)级与A_n、λ_n(n=1,2,…)所表示的(p,q)级之间的等价关系.

The growth of entire functions represented by generalized Laplace-Stiehjes transforms defined in a piecewise smooth jordan curve starting from origin in half right plane is studied. The maximum modulus M（r,F） and the maximum term rn（r,F） of F（s） in the circle ]z[=r are defined. The conception of （p,q） order is introduced. Equivalence relation between （p,q） order represented by maximum modulus M（r,F） and （p,q） order represented by A,, ,A,,（n=1,2,＇..） is then obtained.