A decomposition theorem for BMO and applications
A result of Coifman and Rochberg allows one to decompose an analytic function in the upper half-plane lying in certain function spaces as a sum of coefficients times normalized rational functions, and they showed how to obtain Peller's characterization of trace class Hankel operators from this. The paper under review strengthens the above decomposition theorem by obtaining pointwise estimates on the coefficients. This is used to give pointwise estimates for the singular values of a Hankel operator, the first Calderon commutator, and a product of two Hankel operators, Hankel operators a (converse) estimate that is close to pointwise is given for the derivative of the (Poisson extension of the) symbol in terms of the singular values. A key point is to estimate the singular values of a sum of rank one operators. If the vectors involved are orthonormal this is trivial, but that never happens in real life. The authors introduce a condition (''nearly weakly orthonormal'') that does arise in examples and is good enough to give the right kind of estimates.
Peller's characterization of trace class Hankel operators
singular values of a sum of rank one operators
scientific article; zbMATH DE number 3953624
scientific article