On the Weak-type Constant of the Beurling-Ahlfors Transform

摘要

The Beurling-Ahlfors operator B defined on L~p (C) byrnBf(z) = 1/π p.v. ∫_C f(w)/(z-w)~2 dm(w) (1.1)rnis a well-known example of a Calderon-Zygmund singular integral operator of convolution type. The operator arises naturally in the study of the regularity of solutions of the Beltrami equation and thus has applications to quasiconformal mapping theory and partial differential equations (see [1; 9; 12; 14; 15]).