Degenerate Oscillatory Integral Operators

Project: Research

Wright, James (Principal Investigator)

School of Mathematics

Status	Finished
Effective start/end date	1/01/06 → 31/03/09

Total award	£154,388.00
Funding organisation	EPSRC
Funder project reference	EP/D03289X/1

Period	1/01/06 → 31/03/09

Key findings

We found significant affine-invariant formulations of the Fourier
restriction problem and Lp improving averaging problems along
polynomial curves and establish optimal estimates for both problems.

Research outputs

Strong variational and jump inequalities in harmonic analysis
Research output: Contribution to journal › Article
A variation norm Carleson theorem
Research output: Contribution to journal › Article
Universal L-p improving for averages along polynomial curves in low dimensions
Research output: Contribution to journal › Article
Fourier restriction, polynomial curves and a geometric inequality
Research output: Contribution to journal › Article
Averages in vector spaces over finite fields
Research output: Contribution to journal › Article
Singular integral operators associated to curves with rational components
Research output: Contribution to journal › Article
Fourier restriction to polynomial curves I: a geometric inequality
Research output: Contribution to journal › Article
Weak-type (1,1) bounds for oscillatory singular integrals with rational phases
Research output: Other contribution
Problems on averages and lacunary maximal functions
Research output: Contribution to journal › Article
AN AFFINE-INVARIANT INEQUALITY FOR RATIONAL FUNCTIONS AND APPLICATIONS IN HARMONIC ANALYSIS
Research output: Contribution to journal › Article
Triple Hilbert transforms along polynomial surfaces in R-4
Research output: Contribution to journal › Article