Fractional Besov-Sobolev Spaces on Quasicircles
Abstract
Let $Γ$ be a bounded Jordan curve and $Ω_i,Ω_e$ its two complementary components. For $p\in (1, \infty),\,s\in(0,1)$ we define the two spaces $\mathcal{B}_{p,p}^s(Ω_{i,e})$ as the set of harmonic functions $u$ respectively in $Ω_i$ and $Ω_e$ such that $$ \iint_{Ω_{i,e}} |\nabla u(z)|^p d(z,Γ)^{(1-s)p-1} dxdy
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Harmonic Analysis Research
Analytic and geometric function theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 4 January 2026
- Document type
- Preprint