Year: 2026
Type: article
Abstract: Given a uniform domain , we resolve each element of a suitably defined class of Calderòn–Zygmund (CZ) singular integrals on as a 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 with Lebesgue measure. Our characterization covers the case of compressions to 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 , .
DOI: 10.1112/plms.70231
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Awards: Institute for Computational and Experimental Research in Mathematics, Symmetry Parameter Analysis of Singular Integrals, Singular Integrals with Modulation or Rotational Symmetry, Harmonic analysis of Laplacians in curved spaces, PostDoctoral Research Fellowship, Applications of Harmonic Analysis to Riesz Transforms and Commutators beyond the Classical Settings
OpenAlex ID: W4367365677