Besov spaces and $2$-summing operators
Volume 100 / 2004
Colloquium Mathematicum 100 (2004), 1-8
MSC: 47B10, 47L20, 46E35, 47G10.
DOI: 10.4064/cm100-1-1
Abstract
Let ${\mit \Pi }_{2}$ be the operator ideal of all absolutely $2$-summing operators and let $I_{m}$ be the identity map of the $m$-dimensional linear space. We first establish upper estimates for some mixing norms of $I_{m}$. Employing these estimates, we study the embedding operators between Besov function spaces as mixing operators. The result obtained is applied to give sufficient conditions under which certain kinds of integral operators, acting on a Besov function space, belong to ${\mit \Pi }_{2}$; in this context, we also consider the case of the square ${\mit \Pi }_{2} \circ {\mit \Pi }_{2}$.
