Cauchy non-integral formulas
2014 (English)In: Contemporary Mathematics, Providence, RI; American Mathematical Society; 1999 , 2014, Vol. 612, 163-178 p.Conference paper (Refereed)
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. Rosen. 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 spaces L-2(R-+(1+n), t(alpha) dtdx) also in the case vertical bar alpha vertical bar less than 1. In the end point cases alpha = +/- 1, we show how to apply Carleson duality results by T. Hytonen and A. Rosen to establish such Cauchy formulas.
Place, publisher, year, edition, pages
Providence, RI; American Mathematical Society; 1999 , 2014. Vol. 612, 163-178 p.
IdentifiersURN: urn:nbn:se:liu:diva-106700DOI: 10.1090/conm/612/12230ISI: 000334130600011ISBN: 978-0-8218-9433-0ISBN: 978-1-4704-1525-9OAI: oai:DiVA.org:liu-106700DiVA: diva2:717958
HARMONIC ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS