Quasiconformal symbols and projected composition operators
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912755617890304 |
|---|---|
| author | Sönmez, Sinem Taskinen, Jari |
| author_facet | Sönmez, Sinem Taskinen, Jari |
| contents | We study projected composition operators K_g with quasiconformal symbols g on weighted Bergman spaces on the open unit disc D. If the symbol were conformal, i.e.a Möbius transform of D, the corresponding composition operator would be automatically invertible at least in standard weighted spaces. We show that the invertibility remains, if the Beltrami coefficient is small enough, in particular, it satisfies a certain vanishing condition at the boundary of the disc. We also consider the invertibility of K_g for symbols g which are conformal in an annulus { R < |z| < 1 }. The weight classes in our considerations include both standard and exponentially decreasing weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08473 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasiconformal symbols and projected composition operators Sönmez, Sinem Taskinen, Jari Functional Analysis 47B33, 46E15 We study projected composition operators K_g with quasiconformal symbols g on weighted Bergman spaces on the open unit disc D. If the symbol were conformal, i.e.a Möbius transform of D, the corresponding composition operator would be automatically invertible at least in standard weighted spaces. We show that the invertibility remains, if the Beltrami coefficient is small enough, in particular, it satisfies a certain vanishing condition at the boundary of the disc. We also consider the invertibility of K_g for symbols g which are conformal in an annulus { R < |z| < 1 }. The weight classes in our considerations include both standard and exponentially decreasing weights. |
| title | Quasiconformal symbols and projected composition operators |
| topic | Functional Analysis 47B33, 46E15 |
| url | https://arxiv.org/abs/2512.08473 |