MUCKENHOUPT-WHEEDEN CONJECTURES FOR SPARSE OPERATORS

Abstract. In this talk, we will show an example of a pair of weights (u, v) for which the Hardy-Littlewood maximal function is bounded from Lp(v) to Lp(u) and from Lp! (u1−p! ) to Lp! (v1−p! ) while a dyadic sparse operator is not bounded on the same domain and range. Our construction also provides an example of a single weight for which the weak-type endpoint does not hold for sparse operators.