The Bergman spaces are kernel of CR operators in L^2-spaces on complex domains. We introduce generalisation of Bergman spaces as kernel of higher order covariant  CR operators and study the corresponding Toeplitz operators. We prove they are matrix-valued Toeplitz and we compute their Dixmier traces. These operators can not treated by the standard calculus of Toepltiz operators with elliptic symbols. (Joint work with M. Englis).

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