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Weak and Strong Type [Formula: see text] - [Formula: see text] Estimates for Sparsely Dominated Operators

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We consider operators T satisfying a sparse domination property | &#10216; T f , g &#10217; | &#8804; c &#8721; Q &#8712; S &#10216; f &#10217; p 0 , Q &#10216; g &#10217; q 0 ' , Q | Q | with averaging exponents 1 &#8804; p 0 < q 0 &#8804; &#873... ...