1998/07/16 by Harri Ojanen, Ojanen, Harri
Mathematics · #42B20 #42B25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:42B20 #msc:42B25
paper · pdf · doi:10.48550/arxiv.math/9807085
32 pages, 2 figures
arxiv created 1998/07/16 · arxiv updated 2009/11/30
Weighted norm estimates and representation formulas are proved for non-homogeneous singular integrals with no regularity condition on the kernel and only an L log L integrability condition. The representation formulas involve averages over a star-shaped set naturally associated with the kernel. The proof of the norm estimates is based on the representation formulas, some new variations of the Hardy-Littlewood maximal function, and weighted Littlewood-Paley theory.