Two-dimensional Mikhlin-Calderon-Zygmund operators and bisingular operators (Q1086819)

The author studies algebras of operators geneated by bisingular integral operators, i.e., the typical symbol of such an operator is sgn \(\xi\) \({}_ 1\) or sgn \(\xi\) \({}_ 2\) extended as a function homogeneous of degree 0. The symbols can be piecewise continuous functions on \(S^ 1\) extended to the space as functions homogeneous of degree 0. He classifies the Noetherian operators as those with invertible symbol and gives a formula in terms of the symbol for the index of a Noetherian operator.