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Weighted Weak-type Inequalities For Fractionally Sparsely Dominated Operators

Weighted Weak-type Inequalities For Fractionally Sparsely Dominated Operators

In this paper, we establish quantitative weak type estimates for operators that are dominated by (fractional) sparse operators in bilinear sense. Specifically, we derive bounds for both the restricted weak type $L^{p,1}\rightarrow L^{q,\infty}$ and the multiplier weak type, the latter of which has been previously considered by Cruz-Uribe and Sweeting. …