4 papers
The full range of uniform bounds for the bilinear Hilbert transform
Gennady Uraltsev, Michał Warchalski
We prove uniform uniform bounds for the family of bilinear Hilbert transforms $\mathrm{BHT}_β [f_1, f_2] (x) := \mathrm{p.v.} \int_{\mathbb{R}} f_1 (x - t) f_2 (x + βt) \fr…
Variational Carleson operators in UMD spaces
Alex Amenta, Gennady Uraltsev
We prove -boundedness of variational Carleson operators for functions valued in intermediate UMD spaces. This provides quantitative information on the rate of convergence of p…
The bilinear Hilbert transform in UMD spaces
Alex Amenta, Gennady Uraltsev
We prove -bounds for the bilinear Hilbert transform acting on functions valued in intermediate UMD spaces. Such bounds were previously unknown for UMD spaces that are not Bana…
Banach-valued modulation invariant Carleson embeddings and outer- spaces: the Walsh case
Alex Amenta, Gennady Uraltsev
We prove modulation invariant embedding bounds from Bochner spaces on the Walsh group to outer- spaces on the Walsh extended phase plane. The Banach space…