2020/08/15 by Πέτρος Γαλανόπουλος, Galanopoulos, Petros, Georgios Stylogiannis +1 · 1 citation
Mathematics · #30H20 #46E15 #47B05 #47B10 #47B38 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2008.06684
openalex publication_date 2020/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let μ be a positive Borel measure on the positive real axis. We study the integral operator Hμ(f)(z)=∫0∞(1)/(t)f((z)/(t)) dμ(t), z∈ ℂ , acting on the Fock spaces Fpα, p∈ [1,∞], α>0. Its action is easily seen to be a coefficient multiplication by the moment sequence μn= ∫1∞\frac1tn+1 dμ(t) . We prove that ||Hμ||Fpα→ Fpα=supn∈ℕμn, 1≤ p≤ ∞ . A little-o,condition describes the compactness of Hμ on every Fpα, p∈ (1,∞ ). In addition, we completely characterize the Schatten class membership of Hμ.