Pseudo-holomorphic functions at the critical exponent
Laurent Baratchart
INRIA, Sophia Antipolis, FranceAlexander Borichev
Aix Marseille Université, Marseille, FranceSlah Chaabi
INRIA, Sophia Antipolis, France
![Pseudo-holomorphic functions at the critical exponent cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jems-volume-18-issue-9.png&w=3840&q=90)
Abstract
We study Hardy classes on the disk associated to the equation for with . The paper seems to be the first to deal with the case . We prove an analog of the M. Riesz theorem and a topological converse to the Bers similarity principle. Using the connection between pseudo-holomorphic functions and conjugate Beltrami equations, we deduce well-posedness on smooth domains of the Dirichlet problem with weighted boundary data for 2D isotropic conductivity equations whose coefficients have logarithm in . In particular these are not strictly elliptic. Our results depend on a new multiplier theorem for -functions.
Cite this article
Laurent Baratchart, Alexander Borichev, Slah Chaabi, Pseudo-holomorphic functions at the critical exponent. J. Eur. Math. Soc. 18 (2016), no. 9, pp. 1919–1960
DOI 10.4171/JEMS/634