A nonlinear version of Roth's theorem for sets of positive density in the real line

DOI10.1007/BF02796120zbMath0675.42010OpenAlexW2005734216MaRDI QIDQ1122088

Jean Bourgain

Publication date: 1988

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02796120

zbMATH Keywords

Fourier transformsRoth's theorem

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Special sequences and polynomials (11B83)

Related Items (12)

Trilinear smoothing inequalities and a variant of the triangular Hilbert transform ⋮ Density theorems for anisotropic point configurations ⋮ Some open problems on multiple ergodic averages ⋮ Bilinear Hilbert transforms and (sub)bilinear maximal functions along convex curves ⋮ Pointwise ergodic theorems for non-conventional bilinear polynomial averages ⋮ Nonlinear Roth type theorems in finite fields ⋮ A strong-type Furstenberg-Sárközy theorem for sets of positive measure ⋮ A unified approach to three themes in harmonic analysis. I \& II: I. The linear Hilbert transform and maximal operator along variable curves. II Carleson type operators in the presence of curvature ⋮ A polynomial Roth theorem on the real line ⋮ A general nonlinear version of Roth's theorem on the real line ⋮ Two bipolynomial Roth theorems in \(\mathbb{R}\) ⋮ A nonlinear version of Roth's theorem on sets of fractional dimensions

Cites Work

• A Szemerédi type theorem for sets of positive density in \(\mathbb R^k\)
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