Title: Equivalence of sparse and Carleson coefficients for general sets,
Abstract: We remark that sparse and Carleson coefficients are equivalent for every
countable collection of Borel sets and hence, in particular, for dyadic
rectangles, the case relevant to the theory of bi-parameter singular integrals.
The key observation is that a dual refomulation by I. E. Verbitsky for
Carleson coefficients over dyadic cubes holds also for Carleson coefficients
over general sets. We give a simple proof for this reformulation.