Boundedness of Journé operators with matrix weights

2021/02/05 by Komla Domelevo, Spyridon Kakaroumpas, Domelevo, Komla +5
Mathematics · #42B15 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Primary: 42B20 #Secondary: 42B25 #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2102.03395

openalex publication_date 2021/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a biparameter theory for matrix weights and provide various biparameter matrix-weighted bounds for Journé operators as well as other central operators under the assumption of the product matrix Muckenhoupt condition. In particular, we provide a complete theory for biparameter Journé operator bounds on matrix-weighted L² spaces. We also achieve bounds in the general case of matrix-weighted L^p spaces, for 1 < p < ∞ for paraproduct-free Journé operators. Finally, we expose an open problem involving a matrix-weighted Fefferman--Stein inequality, on which our methods rely in the general setting of matrix-weighted bounds for arbitrary Journé operators and p ≠ 2.

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