Generalized Carleson Embeddings of M{ü}ntz Spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913250153594880 |
|---|---|
| author | Latocca, Mickaël Munnier, Vincent |
| author_facet | Latocca, Mickaël Munnier, Vincent |
| contents | This paper establishes Carleson embeddings of M{ü}ntz spaces $M^q_Λ$ into weighted Lebesgue spaces $L^p(\mathrm{d}μ)$, where $μ$ is a Borel regular measure on $[0,1]$ satisfying $μ([1-\varepsilon])\lesssim \varepsilon^β$. In the case $β\geqslant 1$ we show that such measures are exactly the ones for which Carleson embeddings $L^{\frac{p}β} \hookrightarrow L^p(\mathrm{d}μ)$ hold. The case $β\in (0,1)$ is more intricate but we characterize such measures $μ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00395 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Carleson Embeddings of M{ü}ntz Spaces Latocca, Mickaël Munnier, Vincent Classical Analysis and ODEs Functional Analysis This paper establishes Carleson embeddings of M{ü}ntz spaces $M^q_Λ$ into weighted Lebesgue spaces $L^p(\mathrm{d}μ)$, where $μ$ is a Borel regular measure on $[0,1]$ satisfying $μ([1-\varepsilon])\lesssim \varepsilon^β$. In the case $β\geqslant 1$ we show that such measures are exactly the ones for which Carleson embeddings $L^{\frac{p}β} \hookrightarrow L^p(\mathrm{d}μ)$ hold. The case $β\in (0,1)$ is more intricate but we characterize such measures $μ$ 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. |
| title | Generalized Carleson Embeddings of M{ü}ntz Spaces |
| topic | Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2403.00395 |