Elliptic systems with almost regular coefficients: Singular weight integral operators

We consider the linear elliptic system of two first-order equations partial derivativezw + mu1(z)partial derivativezw + mu2(z) (partial derivative zw) over bar = A(z)w + B(z) (w) over bar + F(z), where w(z, (z) over bar) = u + iv is an unknown complex-valued function, and the related integral operators and boundary value problems. We assume that A, B, F is an element of L-p (Omega), p less than or equal to 2, in contrast to the regular Vekua's theory where p > 2. We prove that in this case the solutions of the system still preserve the properties, which correspond to the regular case with respect to: the structure of zeros, Liouville's theorem, solvability of Riemann-Hilbert boundary value problems etc.