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Cauchy non-integral formulas
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2014 (English)In: Contemporary Mathematics, Providence, RI; American Mathematical Society; 1999 , 2014, Vol. 612, 163-178 p.Conference paper (Refereed)
Abstract [en]

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.
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-106700DOI: 10.1090/conm/612/12230ISI: 000334130600011ISBN: 978-0-8218-9433-0ISBN: 978-1-4704-1525-9OAI: diva2:717958
Available from: 2014-05-19 Created: 2014-05-19 Last updated: 2014-05-21

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Rosén, Andreas
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Mathematics and Applied MathematicsThe Institute of Technology
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