On the iterated Stieltjes transform and its convolution with applications to singular integral equations

S. Yakubovich, M. Martins

Published 2013-11-13, updated 2013-11-25Version 2

We consider mapping properties of the iterated Stieltjes transform, establishing its new relations with the iterated Hilbert transform (a singular integral) on the half-axis and proving the corresponding convolution and Titchmarsh's type theorems. Moreover, the obtained convolution method is applied to solve a new class of singular integral equations.