Factorization in independent sums of Haar system Hardy spaces

2025/07/24 by Konstantos, Konstantinos, Speckhofer, Thomas
#30H10 #46B09 #46B25 #46E30 #47A68 #47L20 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2507.18600

Abstract

We introduce a generalization of the Bourgain-Rosenthal-Schechtman R_ω^p 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 Y_ω as the closed linear span in Y of independent distributional copies of the spaces Y_n of dyadic step functions at scale 2^-n. Combining finite-dimensional and infinite-dimensional techniques, we prove that the identity operator I on Y_ω factors through every bounded linear operator T on Y_ω which has large diagonal, and in general, the identity factors either through T or through I - T.

Citations

• Multipliers on bi-parameter Haar system Hardy spaces
• Factorization Property in Rearrangement Invariant Spaces
• Factorisation in stopping-time Banach spaces: identifying unique maximal ideals
• The space L₁(L_p) is primary for 1
• Subsymmetric bases have the factorization property
• A hereditarily indecomposable L_∞-space that solves the scalar-plus-compact problem
• The unconditional basic sequence problem

Related

• Haar bases on quasi-metric measure spaces, and dyadic structure theorems for function spaces on product spaces of homogeneous type
• Factorization Property in Rearrangement Invariant Spaces
• Multipliers on bi-parameter Haar system Hardy spaces
• Weak factorization of the Hardy space H^p for small values of p, in the multilinear setting
• Coordinate systems and distributional embeddings in Bourgain-Rosenthal-Schechtman spaces: a framework for operator reduction