Annular variation and dyadic absolute bounds for the triangular Hilbert transform
The following describes the scope of the Lean formalization related to the following accompanying paper(s):
Scope
The formalized result proves the symmetric maximal estimate for the triangular Hilbert transform: for arbitrary complex $F,G\in L^3(\mathbb R^2)$, the $L^{3/2}$ norm of the supremum over all finite hard-truncation intervals is at most $C|F|_3|G|_3$ for one absolute constant $C$. It also establishes a common full-measure set on which the truncated integrals are defined and almost-everywhere measurability of the maximal output.
Comparator links
| Result | Comparator statement |
|---|---|
| Maximal triangular Hilbert transform bound | TriangularHilbert.lean |