A norm estimation for the generalized quasitranslation operator by orthogonal polynomials (Q1200380)

For a vector-valued function with values in \(UMD\)-spaces the generalized quasishift operator \(T^ y\) for three orthonormal polynomial systems in introduced. If these systems coincide, the operator \(T^ y\) is called generalized shift operator. Weighted norm inequalities for \(T^ y\) are given. Proofs are based on the representation of the trilinear kernel.