Entropy Bumps and Another Sufficient Condition for the Two--Weight Boundedness of Sparse Operators

In this short note, we give a very efficient proof of a recent result of Treil-Volberg and Lacey--Spencer giving sufficient conditions for the two-weight boundedness of a sparse operator. We also give a new sufficient condition for the two-weight boundedness of a sparse operator. We make critical use of a formula of Hyt\"onen