2014/05/16 by T. Kappeler, Thomas Kappeler, А. М. Савчук +9
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA
paper · pdf · doi:10.48550/arxiv.1405.4253
arxiv created 2014/05/16 · openalex publication_date 2014/05/16 · arxiv updated 2014/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (X0, X1) and (Y0, Y1) be complex Banach couples and assume that X1⊆ X0 with norms satisfying ‖x‖X0 ≤ c‖x‖X1 for some c > 0. For any 0<θ<1, denote by Xθ= [X0, X1]θ and Yθ= [Y0, Y1]θ the complex interpolation spaces and by B(r, Xθ), 0 ≤ θ≤ 1, the open ball of radius r>0 in Xθ, centered at zero. Then for any analytic map Φ: B(r, X0) → Y0+ Y1 such that Φ: B(r, X0)→ Y0 and Φ: B(c-1r, X1)→ Y1 are continuous and bounded by constants M0 and M1, respectively, the restriction of Φ to B(c-θr, Xθ), 0 < θ< 1, is shown to be a map with values in Yθ which is analytic and bounded by M01-θ M1θ.