C*-algebras of Bergman Type Operators with Piecewise Slowly Oscillating Coefficients over Domains with Dini-Smooth Corners

Given a simply connected domain U subset of C with a piecewise Dini-smooth boundary partial derivative U which admits a finite set of Dini-smooth corners of openings lying in (0, 2 pi], we study the C*-algebra B-U = {aI, B-U, (B) over tilde (U) : a is an element of X(L)} generated by the operators of multiplication by functions in X(L), and by the Bergman projection B-U and anti-Bergman projection (B) over tilde (U) acting on the Lebesgue space L-2(U). The C*-algebra X(L) is generated by all piecewise continuous functions on the closure (U) over bar of U with discontinuities on a finite union L of piecewise Dini-smooth curves that have one-sided tangents at every point, do not form cusps and are not tangent to partial derivative U at the points of L boolean AND partial derivative U, and by all bounded continuous functions on U that slowly oscillate at points of partial derivative U. Making use of the Allan-Douglas local principle, the limit operators techniques and the Kehe Zhu results on the class Q = VMO partial derivative(D) boolean AND L-infinity (D), a Fredholm symbol calculus for the C*-algebra B-U is constructed and a Fredholm criterion for the operators A is an element of B-U is obtained.