论文标题
关于一类Volterra积分操作员的加权估计
On weighted estimates for a class of Volterra integral operators
论文作者
论文摘要
Volterra积分运算符$ {\ cal a} = \ sum_ {k = 0}^m {\ cal a} _K $，$（{\ cal a} _k f）（x）= a_k（x）\ int_0^x t_0^x t^k f（x t^k f（t）在权重和函数的某些条件下，$ a_k $，显示出$ \ cal a $在且仅当每个$ {\ cal a} _k $都有边界时。然后，将此结果应用于在$（0，+\ infty）$上的加权Sobolev空间中的点乘积空间。
Volterra integral operators ${\cal A}=\sum_{k=0}^m {\cal A}_k$, $({\cal A}_k f)(x)= a_k (x)\int_0^x t^k f(t) \,dt$, are studied acting between weighted $L_2$ spaces on $(0,+\infty)$. Under certain conditions on the weights and functions $a_k$, it is shown that $\cal A$ is bounded if and only if each ${\cal A}_k$ is bounded. This result is then applied to describe spaces of pointwise multipliers in weighted Sobolev spaces on $(0,+\infty)$.
