A transference approach to estimates of vectorial Hankel operators (Q2761486)

The authors show how the dimensional growth of the constants in the matrix Carleson embedding theorem is related to the dimensional growth of the constants occurring in the estimate of the norm of vectorial Hankel operators in terms of a certain BMO-norm of their symbols. Using the transference technique, the authors show that any ``good'' matrix measure with ``bad'' embedding constant can be used to construct a Hankel operator that is ``good'' on test functions, but has a ``bad'' estimate for the norm. It also should be noted that the argument can be reversed: the existence of a Hankel operator ``good'' on test functions, but having a ``bad'' estimate for the norm implies the existence of a ``good'' matrix measure with ``bad'' embedding constant. In particular, this comparison implies the existence of an operator weight \(W\) such that \(W\) satisfies the operator \(A_2\) condition, but the Hilbert transform on \(L^2(W)\) is unbounded.