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Register a new userSplitting of Volterra Integral Operators with Degenerate Kernels
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Authors
Vyacheslav S. Rychkov
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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 $(0,+infty)$.
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