2023/04/27 by Francesco Di Plinio, Di Plinio, Francesco, A. Walton Green +3
Computer Science · Mathematics · #30C62 (Secondary) #42B20 (Primary) 42B25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2304.13909
openalex publication_date 2023/04/27 · openalex created_date 2023/04/30 · openalex updated_date 2026/08/01
Given a uniform domain Ω⊂ \mathbb Rd, we resolve each element of a suitably defined class of Calderòn-Zygmund (CZ) singular integrals on Ω as the linear combination of Triebel wavelet operators and paraproduct terms. Our resolution formula entails a testing type characterization, loosely in the vein of the David-Journé theorem, of weighted Sobolev space bounds in terms of Triebel-Lizorkin and tree Carleson measure norms of the paraproduct symbols, which is new already in the case Ω=\mathbb Rd with Lebesgue measure. Our characterization covers the case of compressions to Ω of global CZ operators, extending and sharpening past results of Prats and Tolsa for the convolution case. The weighted estimates we obtain, particularized to the Beurling operator on a Lipschitz domain with normal to the boundary in the corresponding sharp Besov class, may be used to deduce quantitative estimates for quasiregular mappings with dilatation in the Sobolev space W1,p(Ω), p>2.