The operators such as
aP PaI , aQ QaI
and integral operators with weak
singularities are studied in the work. It is proven that the operators
continuous (or compact) in spaces with weights in one and only one case, when the function
continuous on the contour of integration. As a corollary, it is shown that the factor-algebra generated by
singular operators with piecewise continuous coefficients is not comutative and the symbol on that algebra
is a matrix-function.
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