2011/12/04 by Yanqi Qiu, Qiu, Yanqi
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.1112.0739
minor revision was made
openalex publication_date 2011/12/04 · arxiv created 2012/06/06 · arxiv updated 2012/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let 1 < p ≠ q < ∞ and (D, μ) = (\± 1\, 1/2 δ-1 + 1/2 δ1). Define by recursion: X0 = \C and Xn+1 = Lp(μ; Lq(μ; Xn)). In this paper, we show that there exist c1=c1(p, q)>1 depending only on p, q and c2 = c2(p, q, s) depending on p, q, s, such that the UMDs constants of Xn's satisfy c1n ≤ Cs(Xn) ≤ c2n for all 1 < s < ∞. Similar results will be showed for the analytic UMD constants. We mention that the first super-reflexive non-UMD Banach lattices were constructed by Bourgain. Our results yield another elementary construction of super-reflexive non-UMD Banach lattices, i.e. the inductive limit of Xn, which can be viewed as iterating infinitely many times Lp(Lq).