论文标题
用退化内核分裂Volterra积分操作员
Splitting of Volterra Integral Operators with Degenerate Kernels
论文作者
论文摘要
Volterra具有非签名定义的脱位核$ a（x，x，t）= \ sum_ {k = 0}^n a_k（x，x，t）$，$ a_k（x，x，t）= a_k（x，x）t^k $的积分运算符，由一个加权$ l_2 $（$ l_2 $ on ote $ l_2 $ on（+fly）进行了研究。在其中一个权重上施加了整体加倍条件，这表明具有内核$ a（x，t）$的运算符在且只有$ n+1 $ a_k $ a_k（x，t）$的情况下是有限的。我们将此结果应用于加权Sobolev空间中$（0，+\ infty）$中的倍增乘数的空间。
Volterra integral operators with non-sign-definite degenerate kernels $A(x,t)= \sum_{k=0}^n A_k(x,t)$, $A_k(x,t)= a_k (x) t^k$, are studied acting from one weighted $L_2$ space on $(0,+\infty)$ to another. Imposing an integral doubling condition on one of the weights, it is shown that the operator with the kernel $A(x,t)$ is bounded if and only $n+1$ operators with kernels $A_k(x,t)$ are all bounded. We apply this result to describe spaces of pointwise multipliers in weighted Sobolev spaces on $(0,+\infty)$.
