Embedding theorems for Müntz spaces

Chalendar, Isabelle, Fricain, Emmanuel, and Timotin, Dan. "Embedding theorems for Müntz spaces." Annales de l’institut Fourier 61.6 (2011): 2291-2311. <http://eudml.org/doc/219799>.

@article{Chalendar2011,
abstract = {We discuss boundedness and compactness properties of the embedding $\{M_\Lambda ^1\}\subset L^1(\mu )$, where $\{M_\Lambda ^1\}$ is the closed linear span of the monomials $x^\{\lambda _n\}$ in $L^1([0,1])$ and $\mu $ is a finite positive Borel measure on the interval $[0,1]$. In particular, we introduce a class of “sublinear” measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences $\Lambda $. Finally, we show how one can recapture some of Al Alam’s results on boundedness and the essential norm of weighted composition operators from $\{M_\Lambda ^1\}$ to $L^1([0,1])$.},
affiliation = {Université de Lyon 1 INSA de Lyon, École Centrale de Lyon CNRS, UMR5208, Institut Camille Jordan 43 bld. du 11 novembre 1918 69622 Villeurbanne Cedex (France); Université de Lyon 1 INSA de Lyon, École Centrale de Lyon CNRS, UMR5208, Institut Camille Jordan 43 bld. du 11 novembre 1918 69622 Villeurbanne Cedex (France); Institute of Mathematics of the Romanian Academy PO Box 1-764 Bucharest 014700 (Romania)},
author = {Chalendar, Isabelle, Fricain, Emmanuel, Timotin, Dan},
journal = {Annales de l’institut Fourier},
keywords = {Müntz space; embedding measure; weighted composition operator; compact operator; essential norm},
language = {eng},
number = {6},
pages = {2291-2311},
publisher = {Association des Annales de l’institut Fourier},
title = {Embedding theorems for Müntz spaces},
url = {http://eudml.org/doc/219799},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Chalendar, Isabelle
AU - Fricain, Emmanuel
AU - Timotin, Dan
TI - Embedding theorems for Müntz spaces
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 6
SP - 2291
EP - 2311
AB - We discuss boundedness and compactness properties of the embedding ${M_\Lambda ^1}\subset L^1(\mu )$, where ${M_\Lambda ^1}$ is the closed linear span of the monomials $x^{\lambda _n}$ in $L^1([0,1])$ and $\mu $ is a finite positive Borel measure on the interval $[0,1]$. In particular, we introduce a class of “sublinear” measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences $\Lambda $. Finally, we show how one can recapture some of Al Alam’s results on boundedness and the essential norm of weighted composition operators from ${M_\Lambda ^1}$ to $L^1([0,1])$.
LA - eng
KW - Müntz space; embedding measure; weighted composition operator; compact operator; essential norm
UR - http://eudml.org/doc/219799
ER -