Mixed-norm bounds for circular averages on α-dimensional fractals yield the first exceptional set estimates for Hölder regularity of linear wave solutions in R².
On maximal functions associated to families of curves in the plane
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Bilinear Kakeya inequality established in the Heisenberg group via reduction to sharp curved-tube estimates in R^2, supported by a novel broadness hypothesis.
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Weighted mixed-norm estimates for circular averages and exceptional set estimates for the wave equation
Mixed-norm bounds for circular averages on α-dimensional fractals yield the first exceptional set estimates for Hölder regularity of linear wave solutions in R².
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A Bilinear Kakeya Inequality in the Heisenberg Group
Bilinear Kakeya inequality established in the Heisenberg group via reduction to sharp curved-tube estimates in R^2, supported by a novel broadness hypothesis.