On the boundedness of generalized Cesàro operators on Sobolev spaces

Carlos Lizama, Pedro J. Miana, Rodrigo Ponce +1

For $\beta >0$ and $p\ge 1$, the generalized Cesàro operator $${\mathcal{C}}_{\beta }f(t):=\frac{\beta }{t^{\beta }}{\int }_0^t(t-s{)}^{\beta -1}f(s)ds$$ and its companion operator ${\mathcal{C}}_{\beta }^{\ast }$ defined on Sobol…