加权双线性Hardy算子在加幂权L^p空间中的最佳常数

SHARP BOUND FOR THE WEIGHTED BILINEAR HARDY OPERATOR ON THE LPSPACE WITH POWER WEIGHT

本文研究了加权双线性Hardy算子和加权双线性Cesaro算子在加幂权L^p空间中的有界性,精确得到了这两类算子在加幂权L^p空间中的算子范数.作为应用,得到了双线性Riemann-Liouville算子和双线性Weyl算子的最佳常数.

We study the boundedness of the weighted bilinear Hardy operator and the weighted bilinear Cesaro operator on the Lpspace with power weight and obtain norms of these two operators on the Lpspace with power weight.As applications,we also calculate sharp bounds of the bilinear Riemann-Liouville operator and the bilinear Weyl operator on the L^p space with power weight.