A one parameter family of Volterra-type operators

Francesco Battistoni, Giuseppe Molteni

For every $\alpha \in (0,+\infty )$ and $p,q\in (1,+\infty )$ let $T_{\alpha }$ be the operator $L^p[0,1]\to L^q[0,1]$ defined via the equality $(T_{\alpha }f)(x):={\int }_0^{x^{\alpha }}f(y)dy$. We study the…