Generalized Carleson Embeddings of Müntz Spaces - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

Generalized Carleson Embeddings of Müntz Spaces

Vincent Munnier
  • Fonction : Auteur

Résumé

This paper establishes Carleson embeddings of Müntz spaces $M^q_{\Lambda}$ into weighted Lebesgue spaces $L^p(\mathrm{d}\mu)$, where $\mu$ is a Borel regular measure on $[0,1]$ satisfying $\mu([1-\varepsilon])\lesssim \varepsilon^{\beta}$. In the case $\beta \geqslant 1$ we show that such measures are exactly the ones for which Carleson embeddings $L^{\frac{p}{\beta}} \hookrightarrow L^p(\mathrm{d}\mu)$ hold. The case $\beta \in (0,1)$ is more intricate but we characterize such measures $\mu$ in terms of a summability condition on their moments. Our proof relies on a generalization of $L^p$ estimates à la Gurariy-Macaev in the weighted $L^p$ spaces setting, which we think can be of interest in other contexts.
Fichier principal
Vignette du fichier
final.pdf (318.82 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04485003 , version 1 (01-03-2024)

Identifiants

Citer

Mickaël Latocca, Vincent Munnier. Generalized Carleson Embeddings of Müntz Spaces. 2024. ⟨hal-04485003⟩
16 Consultations
4 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More