Український математичний конгрес - 2009

Yuriy Karlovych (Universidad Autуnoma del Estado de Morelos, Morelos, Mexico)

Boundary value problems with non-regular data

The talk is devoted to studying the Riemann, Hilbert and Haseman boundary value problems for analytic functions in case of non-regular data. Making use of corresponding integral representations, we reduce these problems to local or non-local singular integral equations with discontinuous coefficients on Lebesgue spaces with Muckenhoupt weights over Carleson curves. Applying the theory of pseudo-differential operators with non-regular symbols, we establish Fredholm criteria and index formulas for mentioned boundary value problems. Additional information and comments: Please, send me an invitation letter to postal address indicated above.