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.
SharpL 2 estimates of the Schr¨ odinger maximal function in higher dimensions.Ann
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Under dim_H E >1, dim_H E + dim_H F >2 and F regular (equal Hausdorff and packing dimensions), there exists y in F such that the pinned distance set Δ_y(E) has positive Lebesgue measure.
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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.