2020/06/10 by Emil Airta, Airta, Emil, Henri Martikainen +3
Mathematics · #42B20 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2006.05807
openalex publication_date 2020/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a framework based on modified dyadic shifts to prove multiple results of modern singular integral theory under mild kernel regularity. Using new optimized representation theorems we first revisit a result of Figiel concerning the UMD-extensions of linear Calderón-Zygmund operators with mild kernel regularity and extend our new proof to the multilinear setting improving recent UMD-valued estimates of multilinear singular integrals. Next, we develop the product space theory of the multilinear singular integrals with modified Dini-type assumptions, and use this theory to prove bi-parameter weighted estimates and two-weight commutator estimates.