Lobesgue型函数的精确阶

ON THE EXACT ORDER OF LEBESGUE TYPE FUNCTION

给出λｎ（ｘ）＝ｎｋ＝１｜ｚ－ｘｋ｜ｓ｜ｌｋ（ｘ）｜ｔ和它的更广泛形式∧ｎ（ｘ）＝ｊｎｋ＝ｉｎ｜ｘ－ｘｋ｜ｓ｜ｌｋ（ｘ）｜ｔ的精确阶，它们分别是１ｎｉ－１和１ｍｔ－１ｎ，其中ｓ，ｔ是满足ｓ≥ｔ≥１的固定实数，１≤ｉｎ≤ｊｎ≤ｎ，ｍｎ＝ｊｎ－ｉｎ＋１。

In this paper we give the exact order of λ n(x)=n k=1 |x-x k| s|l k(x)| t and ∧ n(x)= j n k=i n |x-x k| s|l k(x)| t for any fixed real numbers s and t satisfied s≥t≥1, which are 1n t-1 and 1(j n-i n+1) t-1 respectively.