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Directional maximal operators in the plane
This monograph investigates the Lebesgue boundedness of planar directional maximal operators $D_Ω$. These are maximal averages of functions over line segments in $\mathbb R^2$ whose slopes lie in a specified set $Ω\subseteq\mathbb R$. A large body of work has identified a geometric property of $Ω$,
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