Quantitative weighted estimates for rough homogeneous singular integrals

• Published in: Israel journal of mathematics Vol. 218; no. 1; pp. 133 - 164
• Main Authors: Hytönen, Tuomas P., Roncal, Luz, Tapiola, Olli
• Format: Journal Article
• Language: English
• Published: Jerusalem The Hebrew University Magnes Press 01.03.2017; Springer Nature B.V
• Subjects: Algebra; Analysis; Applications of Mathematics; Decomposition; Group Theory and Generalizations; Integrals; Kernels; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Operators (mathematics); Series expansion; Theoretical

We consider homogeneous singular kernels, whose angular part is bounded, but need not have any continuity. For the norm of the corresponding singular integral operators on the weighted space L 2 ( w ), we obtain a bound that is quadratic in A 2 constant [ w ] A 2 . We do not know if this is sharp, b...