2023/11/02 by Pascal Lefèvre, Daniel Li, Lefèvre, Pascal +5
Mathematics · #Holomorphic and Operator Theory #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis
paper · pdf · doi:10.48550/arxiv.2311.01062
We first consider some questions raised by N. Zorboska in her thesis. In particular she asked for which sequences β every symbol φ\colon \mathbbD → \mathbbD with φ∈ H2 (β) induces a bounded composition operator Cϕ on the weighted Hardy space H2 (β). We give partial answers and investigate when H2 (β) is an algebra. We answer negatively another question in showing that there are a sequence β and φ∈ H2 (β) such that ‖ φ‖_∞ < 1 and the composition operator Cφ is not bounded on H2 (β). In a second part, we show that for p ≠ 2, no automorphism of \mathbbD, except those that fix 0, induces a bounded composition operator on the Beurling-Sobolev space ℓpA, and even on any weighted version of this space.