On Hille-Tamarkin Operators And Schatten Classes

Abstract

We determine the smallest Schatten class containing all integral operators with kernels in L(p)(L(p',q))symm, where 2 < p < infinity and 1 less-than-or-equal-to q less-than-or-equal-to infinity. In particular, we give a negative answer to a problem posed by Arazy, Fisher, Janson and Peetre in [1].