Eigenvalues of Hille-Tamarkin operators and geometry of Banach function spaces

@article{ThomasKühn2011,
abstract = {We investigate how the asymptotic eigenvalue behaviour of Hille-Tamarkin operators in Banach function spaces depends on the geometry of the spaces involved. It turns out that the relevant properties are cotype p and p-concavity. We prove some eigenvalue estimates for Hille-Tamarkin operators in general Banach function spaces which extend the classical results in Lebesgue spaces. We specialize our results to Lorentz, Orlicz and Zygmund spaces and give applications to Fourier analysis. We are also able to show the optimality of our eigenvalue estimates in the Lorentz spaces $L_\{2,q\}$ with 1 ≤ q < 2 and in Zygmund spaces $L_\{p\}(log L)_a$ with 2 ≤ p < ∞ and a > 0.},
author = {Thomas Kühn, Mieczysław Mastyło},
journal = {Studia Mathematica},
keywords = {eigenvalues; integral operators; Banach function spaces; Lorentz spaces; Orlicz spaces; Zygmund spaces; -concavity; cotype },
language = {eng},
number = {3},
pages = {275-296},
title = {Eigenvalues of Hille-Tamarkin operators and geometry of Banach function spaces},
url = {http://eudml.org/doc/285726},
volume = {207},
year = {2011},
}

TY - JOUR
AU - Thomas Kühn
AU - Mieczysław Mastyło
TI - Eigenvalues of Hille-Tamarkin operators and geometry of Banach function spaces
JO - Studia Mathematica
PY - 2011
VL - 207
IS - 3
SP - 275
EP - 296
AB - We investigate how the asymptotic eigenvalue behaviour of Hille-Tamarkin operators in Banach function spaces depends on the geometry of the spaces involved. It turns out that the relevant properties are cotype p and p-concavity. We prove some eigenvalue estimates for Hille-Tamarkin operators in general Banach function spaces which extend the classical results in Lebesgue spaces. We specialize our results to Lorentz, Orlicz and Zygmund spaces and give applications to Fourier analysis. We are also able to show the optimality of our eigenvalue estimates in the Lorentz spaces $L_{2,q}$ with 1 ≤ q < 2 and in Zygmund spaces $L_{p}(log L)_a$ with 2 ≤ p < ∞ and a > 0.
LA - eng
KW - eigenvalues; integral operators; Banach function spaces; Lorentz spaces; Orlicz spaces; Zygmund spaces; -concavity; cotype
UR - http://eudml.org/doc/285726
ER -