On weighted estimates for a class of Volterra integral operators

Abstract

Volterra integral operators $\mathcal{A}={\sum }_{k=0}^m{\mathcal{A}}_k$, $({\mathcal{A}}_{k}f)(x)=a_k(x){\int }_0^x{t}^{k}f(t)dt$, 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 $\mathcal{A}$ is bounded if and only if each ${\mathcal{A}}_k$ is bounded. This result is then applied to describe spaces of pointwise multipliers in weighted Sobolev spaces on $(0,+\infty )$.

5 pages

References in corpus (2)

• Splitting of Volterra Integral Operators with Degenerate Kernels
• Some weighted Hardy-type inequalities and applications