This article develops a novel approach to the representation of singular integral operators Calderón–Zygmund type in terms continuous model operators, both classical and bi-parametric setting. The is realized as finite sum averages wavelet projections either cancellative or noncancellative type, which are themselves operators. Both properties out reach for established dyadic-probabilistic techn...

In order to characterise the C∗ -algebra generated by the singular Bochner-Martinelli integral over a smooth closed hypersurfaces in C, we compute its principal symbol. We show then that the Szegö projection belongs to the strong closure of the algebra generated by the singular Bochner-Martinelli integral. Mathematics Subject Classification (2000). Primary 32A25; Secondary 47L15, 47G30.

In present paper we elaborated the numerical schemes of iterative methods for an approximate solution of weak singular integral equations with logarithmic Kernel. The equation is examined in a pair of spaces. The results obtained could be used for any pair of the functional spaces where the problem of finding the solution of weak singular integral equations is correctly formulated problem by Ti...