An upper bound on the Kolmogorov widths of a certain family of integral operators

Duaine Lewis, Bernd Sing

We consider the family of integral operators $(K_{\alpha }f)(x)$ from $L^p[0,1]$ to $L^q[0,1]$ given by $$(K_{\alpha }f)(x)={\int }_0^1(1-xy{)}^{\alpha -1}f(y)dy,0<\alpha <1.$$ The mai…