2008/01/11 by Stefano Meda, Meda, S., Peter Sjögren +3
Mathematics · #42B30 #46A22 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.0801.1745
openalex publication_date 2008/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that if q is in (1,∞), Y is a Banach space and T is a linear operator defined on the space of finite linear combinations of (1,q)-atoms in Rn which is uniformly bounded on (1,q)-atoms, then T admits a unique continuous extension to a bounded linear operator from H1(Rn) to Y. We show that the same is true if we replace (1,q)-atoms with continuous (1,∞)-atoms. This is known to be false for (1,∞)-atoms.