Besov spaces and 2-summing operators

M. A. Fugarolas. "Besov spaces and 2-summing operators." Colloquium Mathematicae 100.1 (2004): 1-8. <http://eudml.org/doc/283659>.

@article{M2004,
abstract = {Let Π₂ 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 Π₂; in this context, we also consider the case of the square Π₂ ∘ Π₂.},
author = {M. A. Fugarolas},
journal = {Colloquium Mathematicae},
keywords = {Besov spaces; mixing operators; absolutely 2-summing operators; integral operators},
language = {eng},
number = {1},
pages = {1-8},
title = {Besov spaces and 2-summing operators},
url = {http://eudml.org/doc/283659},
volume = {100},
year = {2004},
}

TY - JOUR
AU - M. A. Fugarolas
TI - Besov spaces and 2-summing operators
JO - Colloquium Mathematicae
PY - 2004
VL - 100
IS - 1
SP - 1
EP - 8
AB - Let Π₂ 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 Π₂; in this context, we also consider the case of the square Π₂ ∘ Π₂.
LA - eng
KW - Besov spaces; mixing operators; absolutely 2-summing operators; integral operators
UR - http://eudml.org/doc/283659
ER -