Splitting of Volterra Integral Operators with Degenerate Kernels

Abstract

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 $(0,+\infty )$.

21 pages

Cited by in corpus (2)

• Some weighted Hardy-type inequalities and applications
• On weighted estimates for a class of Volterra integral operators