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math.CA2004★ 1 cited
Rubio de Francia Littlewood Paley Inequalities and Directional Maximal Functions
Grigor Karagulyan, Michael T Lacey
In , define a maximal function in the directions $v\in \directions\subset\{x \mid \abs x=1\}$ by $$ M^\directions f(x)=\sup_{v\in\directions} \sup_{\zve} \int_{-\ze}^\ze \abs{…
math.CA2004★ 9 cited
An Estimate of the Maximal Operators Associated with Generalized Lacunary Sets
Grigor Karagulyan, Michael T Lacey
Let be any set of directions (unit vectors) on the plane. In this paper we study maximal operator of the one dimensional maximal function computed in the directions of We a…