Stein's theorem in the upper-half plane and Bergman spaces with weights
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915355094417408 |
|---|---|
| author | Bonami, Aline Grellier, Sandrine Sehba, Benoît |
| author_facet | Bonami, Aline Grellier, Sandrine Sehba, Benoît |
| contents | This is a companion paper to our previous one, Avatars of Stein's Theorem in the complex setting. In this previous paper, we gave a sufficient condition for an integrable function in the upper-half plane to have an integrable Bergman projection. Here we push forward methods and establish in particular a converse statement. This naturally leads us to study a family of weighted Bergman spaces for logarithmic weights (1 + ln + (1/___m(z)) + ln + (|z|)) k , which have the same kind of behavior respectively at the boundary and at infinity. We introduce their duals, which are logarithmic Bloch type spaces and interest ourselves in multipliers, pointwise products and Hankel operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18377 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stein's theorem in the upper-half plane and Bergman spaces with weights Bonami, Aline Grellier, Sandrine Sehba, Benoît Classical Analysis and ODEs This is a companion paper to our previous one, Avatars of Stein's Theorem in the complex setting. In this previous paper, we gave a sufficient condition for an integrable function in the upper-half plane to have an integrable Bergman projection. Here we push forward methods and establish in particular a converse statement. This naturally leads us to study a family of weighted Bergman spaces for logarithmic weights (1 + ln + (1/___m(z)) + ln + (|z|)) k , which have the same kind of behavior respectively at the boundary and at infinity. We introduce their duals, which are logarithmic Bloch type spaces and interest ourselves in multipliers, pointwise products and Hankel operators. |
| title | Stein's theorem in the upper-half plane and Bergman spaces with weights |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2506.18377 |