Edward Kroc

most citedLacunarity, Kakeya-type sets and directional maximal operators

4 citations · 4 across the 3 of their papers we have counts for

collaborators

3 papers

math.CA2026

Directional maximal operators in the plane

Edward Kroc, Juyoung Lee, Malabika Pramanik

This monograph investigates the Lebesgue boundedness of planar directional maximal operators $D_{Ω}$ . These are maximal averages of functions over line segments in $R^{2}$ whos…

math.CA2014★ 4 cited

Lacunarity, Kakeya-type sets and directional maximal operators

Edward Kroc, Malabika Pramanik

We develop a notion of finite order lacunarity for direction sets in $R^{d + 1}$ . Given a direction set $Ω$ that is sublacunary according to this definition, we construct ran…

math.CA2014

Kakeya-type sets over Cantor sets of directions in $R^{d + 1}$

Edward Kroc, Malabika Pramanik

Given a Cantor-type subset $Ω$ of a smooth curve in $R^{d + 1}$ , we construct examples of sets that contain unit line segments with directions from $Ω$ and exhibit analytical…

Directional maximal operators in the plane

Lacunarity, Kakeya-type sets and directional maximal operators

Kakeya-type sets over Cantor sets of directions in Rd+1

Kakeya-type sets over Cantor sets of directions in $R^{d + 1}$