Cauchy non-integral formulas
Journal article, 2014

We study certain generalized Cauchy integral formulas for gradients of solutions to second order divergence form elliptic systems, which appeared in recent work by P. Auscher and A. Rosén. These are constructed through functional calculus and are in general beyond the scope of singular integrals. More precisely, we establish such Cauchy formulas for solutions u with gradient in weighted L_2(\R^{1+n}_+, t^{\alpha}dtdx) also in the case |\alpha|<1. In the end point cases \alpha= \pm 1, we show how to apply Carleson duality results by T. Hytönen and A. Rosén to establish such Cauchy formulas.

Author

Andreas Rosén

Contemporary Mathematics

0271-4132 (ISSN) 1098-3627 (eISSN)

Vol. 612 163-178

Subject Categories

Mathematics

DOI

10.1090/conm/612/12230

More information

Created

10/10/2017