Factorization in independent sums of Haar system Hardy spaces
Abstract
We introduce a generalization of the Bourgain–Rosenthal–Schechtman Rωp space: Let Y be a Haar system Hardy space (i.e., a separable rearrangement-invariant function space on the unit interval or an associated Hardy space defined via the square function, such as dyadic H1). Then we define Yω as the closed linear span in Y of independent distributional copies of the spaces Yn of dyadic step functions at scale 2−n. Combining finite-dimensional and infinite-dimensional techniques, we prove that the identity operator I on Yω factors through every bounded linear operator T on Yω that has large diagonal, and in general, the identity factors either through T or through I−T.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
advanced mathematical theories
Advanced Mathematical Physics Problems
Publication details
- Journal / source
- Illinois Journal of Mathematics
- Publisher
- Duke University Press
- Volume
- 70
- Issue
- 2
- Pages
- 277-312
- Publication date
- 1 June 2026
- Language
- EN