Measurable sets in [0,R]² avoiding upward right triangles of area 1/2 satisfy |A| = O_c(R²/(log R)^c) for c<1/4 with Ω(R log R) example; for fixed-area triangles the bound sharpens to c<1/2 using a hyperbolic trilinear smoothing inequality and scale induction.
A short proof on the boundedness of triangular Hilbert transform along curves
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
math.CA 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Compact sets on the real line with large Hausdorff dimension contain curved three-point progressions for nonlinear functions such as polynomials with zero constant term and t^k log(1+t).
citing papers explorer
-
On hyperbolic corners and unit-area triangles in planar sets of large measure
Measurable sets in [0,R]² avoiding upward right triangles of area 1/2 satisfy |A| = O_c(R²/(log R)^c) for c<1/4 with Ω(R log R) example; for fixed-area triangles the bound sharpens to c<1/2 using a hyperbolic trilinear smoothing inequality and scale induction.
-
A curved three-point pattern problem for fractal sets on the real line
Compact sets on the real line with large Hausdorff dimension contain curved three-point progressions for nonlinear functions such as polynomials with zero constant term and t^k log(1+t).