Dense subsets of [N]^n contain configurations x, x + r^{m1}e1, ..., x + r^{mn}en for any fixed n and increasing exponents m_i, with density threshold (log N)^{-c}.
A MULTIDIMENSIONAL SZEMER ´EDI THEOREM 31
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
verdicts
UNVERDICTED 4representative citing papers
Extends Ionescu-Wainger multiplier theorem to weighted and seminorm settings with non-uniform bounds and applies it to Bourgain's polynomial ergodic theorem.
Establishes L^p bound for multi-linear maximal operator along homogeneous polynomial curves under exponent conditions.
New proof of the ℓ²(ℤ^d) boundedness of Bourgain's maximal inequality for Radon polynomial averages via TT* methods.
citing papers explorer
-
A multidimensional Szemer\'{e}di theorem in integers
Dense subsets of [N]^n contain configurations x, x + r^{m1}e1, ..., x + r^{mn}en for any fixed n and increasing exponents m_i, with density threshold (log N)^{-c}.
-
Remarks on the Ionescu-Wainger multiplier theorem
Extends Ionescu-Wainger multiplier theorem to weighted and seminorm settings with non-uniform bounds and applies it to Bourgain's polynomial ergodic theorem.
-
On Multi-linear Maximal Operators Along Homogeneous Curves
Establishes L^p bound for multi-linear maximal operator along homogeneous polynomial curves under exponent conditions.
-
Discrete analogues in harmonic analysis: $TT^*$ methods
New proof of the ℓ²(ℤ^d) boundedness of Bourgain's maximal inequality for Radon polynomial averages via TT* methods.