Abstract
Let M denote the dyadic Maximal Function. We show that there is a weight w, and Haar multiplier T for which the following weak-type inequality fails sup t > 0 t w ( { x ∈ R : | T f ( x ) | > t } ) ⩽ C ∫ R | f | M w ( x ) d x . (With T replaced by M, this is a well-known fact.) This shows that a dyadic version of the so-called Muckenhoupt–Wheeden Conjecture is false. This accomplished by using current techniques in weighted inequalities to show that a particular L 2 consequence of the inequality above does not hold.
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