119 citations · 291 across the 19 of their papers we have counts for
6 papers · 1 filter
On Trilinear Oscillatory Integrals
Michael Christ, Diogo Oliveira e Silva
We examine a certain class of trilinear integral operators which incorporate oscillatory factors e^{iP}, where P is a real-valued polynomial, and prove smallness of such integrals…
Multilinear Oscillatory Integrals Via Reduction of Dimension
Michael Christ
Christ, Li, Tao, and Thiele have established multilinear oscillatory integral operator inequalities under severe dimensional restrictions. These restrictions are relaxed substantia…
Bounds For Multilinear Sublevel Sets Via Szemeredi's Theorem
Michael Christ
In 2005, Li, Tao, Thiele and the author raised a general question concerning upper bounds for a class of multilinear oscillatory integral operators, and established such bounds in…
On extremals for a Radon-like transform
Michael Christ
Convolution with an appropriate surface measure on a paraboloid in R^d defines a bounded operator T from L^p(R^d) to L^q(R^d) for certain exponents p,q. In this article it is prove…
Quasiextremals for a Radon-like transform
Michael Christ
Convolution with an appropriate surface measure on a paraboloid is known to define a bounded operator T from L^p(R^d) to L^q(R^d) for certain exponents p,q. By a quasiextremal for…
Extremizers of a Radon transform inequality
Michael Christ
The Radon transform is a bounded operator from L^p of Euclidean space R^d to L^q of the Grassmann manifold of all affine hyperplanes in R^d, for certain exponents. We identify all…