In this paper we prove that is almost isometric to in the canonical way when is lacunary with a large ratio. On the other hand, our approach can be used to study also the Carleson measures for Müntz spaces when is lacunary. We give some necessary and some sufficient conditions ensuring that a Carleson embedding is bounded or compact. In the hilbertian case, the membership to Schatten classes is also studied. When behaves like a geometric sequence the results are sharp, and we get some characterizations.
Dans cet article, nous montrons que est presque isométrique à , et ce de façon naturelle, lorsque est lacunaire avec une raison grande. Par ailleurs, notre approche permet aussi d’étudier les mesures de Carleson pour les espaces Müntz lorsque est lacunaire. Nous donnons des conditions nécessaires et des conditions suffisantes qui permettent d’assurer qu’un plongement de Carleson est borné ou compact. Dans le cadre hilbertien, nous étudions aussi l’appartenance de ce plongement aux classes de Schatten. Nous obtenons des caractérisations complètes lorsque se comporte comme une suite géométrique.
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Keywords: Müntz spaces, Carleson embeddings, lacunary sequences, Schatten classes
Mot clés : Espaces de Müntz, plongements de Carleson, suites lacunaires, classes de Schatten
@article{AIF_2018__68_5_2215_0, author = {Gaillard, Lo{\"\i}c and Lef\`evre, Pascal}, title = {Lacunary {M\"untz} spaces: isomorphisms and {Carleson} embeddings}, journal = {Annales de l'Institut Fourier}, pages = {2215--2251}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {68}, number = {5}, year = {2018}, doi = {10.5802/aif.3207}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.3207/} }
TY - JOUR AU - Gaillard, Loïc AU - Lefèvre, Pascal TI - Lacunary Müntz spaces: isomorphisms and Carleson embeddings JO - Annales de l'Institut Fourier PY - 2018 SP - 2215 EP - 2251 VL - 68 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.3207/ DO - 10.5802/aif.3207 LA - en ID - AIF_2018__68_5_2215_0 ER -
%0 Journal Article %A Gaillard, Loïc %A Lefèvre, Pascal %T Lacunary Müntz spaces: isomorphisms and Carleson embeddings %J Annales de l'Institut Fourier %D 2018 %P 2215-2251 %V 68 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.3207/ %R 10.5802/aif.3207 %G en %F AIF_2018__68_5_2215_0
Gaillard, Loïc; Lefèvre, Pascal. Lacunary Müntz spaces: isomorphisms and Carleson embeddings. Annales de l'Institut Fourier, Volume 68 (2018) no. 5, pp. 2215-2251. doi : 10.5802/aif.3207. http://archive.numdam.org/articles/10.5802/aif.3207/
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