Geodesic
Besov spaces and $2$-summing operators
M. A. Fugarolas1
1 Departamento de Analisis Matematico Facultad de Matematicas Universidad de Santiago de Compostela Campus Universitario Sur 15782 Santiago de Compostela, Spain
Colloquium Mathematicum, Tome 100 (2004) no. 1, pp. 1-8

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 ${\mit \Pi }_{2} \circ {\mit \Pi }_{2}$.
DOI : 10.4064/cm100-1-1
Keywords: mit operator ideal absolutely summing operators identity map m dimensional linear space first establish upper estimates mixing norms employing these estimates study embedding operators between besov function spaces mixing operators result obtained applied sufficient conditions under which certain kinds integral operators acting besov function space belong mit context consider the square mit circ mit

M. A. Fugarolas 1

1 Departamento de Analisis Matematico Facultad de Matematicas Universidad de Santiago de Compostela Campus Universitario Sur 15782 Santiago de Compostela, Spain 
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M. A. Fugarolas. Besov spaces and $2$-summing operators. Colloquium Mathematicum, Tome 100 (2004) no. 1, pp. 1-8. doi: 10.4064/cm100-1-1

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