Pseudo-holomorphic functions at the critical exponent

الأصل · EN

We study Hardy classes on the disk associated to the equation w=α w for α∈ Lʳ with 2≤ r<∞. The paper seems to be the first to deal with the case r=2. 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 Lᵖ boundary data for 2-D isotropic conductivity equations whose coefficients have logarithm in W¹,². In particular these are not strictly elliptic. Our results depend on a new multiplier theorem for W¹,²₀-functions.