A universal Stein-Tomas restriction estimate for measures in three dimensions
Abstract
We study restriction estimates in R3 for surfaces given as graphs of W11(R2) (integrable gradient) functions. We obtain a "universal" L2(mu) -> L4(R3, L2(SO(3))) estimate for the extension operator f -> f mu in three dimensions. We also prove that the three dimensional estimate holds for any Frostman measure supported on a compact set of Hausdorff dimension greater than two. The approach is geometric and is influenced by a connection with the Falconer distance problem.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.