Boundary limits for bounded quasiregular mappings
| dc.creator | Li, Bao Qin | |
| dc.creator | Villamor, Enrique | |
| dc.date | 2005-07-26 | |
| dc.date.accessioned | 2026-07-07T05:22:01Z | |
| dc.date.available | 2026-07-07T05:22:01Z | |
| dc.description | In this paper we establish results on the existence of nontangential limits for weighted $\Cal A$-harmonic functions in the weighted Sobolev space $W_w^{1,q}(\Bbb B^n)$, for some $q>1$ and $w$ in the Muckenhoupt $A_q$ class, where $\Bbb B^n$ is the unit ball in $\Bbb R^n$. These results generalize the ones in section \S3 of [KMV], where the weight was identically equal to one. Weighted $\Cal A$-harmonic functions are weak solutions of the partial differential equation $$\text{div}(\Cal A(x,\nabla u))=0,$$ where $αw(x) |ξ|^{q} \le < \Cal A(x,ξ),ξ>\le βw(x) |ξ|^{q}$ for some fixed $q\in (1,\infty)$, where $0<α\leq β<\infty$, and $w(x)$ is a $q$-admissible weight as in Chapter 1 in [HKM]. Later, we apply these results to improve on results of Koskela, Manfredi and Villamor [KMV] and Martio and Srebro [MS] on the existence of radial limits for bounded quasiregular mappings in the unit ball of $\Bbb R^n$ with some growth restriction on their multiplicity function. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0507540 | |
| dc.identifier | http://arxiv.org/abs/math/0507540 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75902 | |
| dc.subject | Complex Variables | |
| dc.subject | 31B25 | |
| dc.title | Boundary limits for bounded quasiregular mappings | |
| dc.type | text |