Besov spaces and $2$-summing operators

Volume 100 / 2004

M. A. Fugarolas Colloquium Mathematicum 100 (2004), 1-8 MSC: 47B10, 47L20, 46E35, 47G10. DOI: 10.4064/cm100-1-1


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 ${\mit \Pi }_{2} \circ {\mit \Pi }_{2}$.


  • M. A. FugarolasDepartamento de Analisis Matematico
    Facultad de Matematicas
    Universidad de Santiago de Compostela
    Campus Universitario Sur
    15782 Santiago de Compostela, Spain

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