Calderón's Problem for Lipschitz Classes and the Dimension of Quasicircles

Abstract

In the last years the mapping properties of the Cauchy integral CGf(z) = 1/(2pi) ?G [f(?) / ? - z] d? have been widely studied. The most important question in this area was Calderon's problem, to determine those rectifiable Jordan curves G for which CG defines a bounded operator on L2(G). The question was solved by Guy David [Da] who proved that CG is bounded on L2(G) (or on Lp(G), 1 < p < 8) if and only if G is regular, i.e., H1(G n B(z0,R) = CR for every z0 I C, R > 0 and for some constant C (...).

Locations

• Revista Matemática Iberoamericana - View - PDF