# Degenerate Oscillatory Integral Operators

Lead Research Organisation:
University of Edinburgh

Department Name: Sch of Mathematics

### Abstract

In recent years, Fourier Analysis on Euclidean Spaces has become an extremely active research area in the USA and Europe and many of the centralproblems in this area can be reduced to understanding various oscillatory integral operators. The underlying geometry of the problemoften makes the corresponding operator degenerate in a certain sense. In thisproject we aim to explore and understand degenerateoscillatory integral operators which arise in keyresearch areas.

## People |
## ORCID iD |

James Wright (Principal Investigator) |

### Publications

CARBERY A
(2008)

*Averages in vector spaces over finite fields*in Mathematical Proceedings of the Cambridge Philosophical Society
Dendrinos S
(2010)

*An affine-invariant inequality for rational functions and applications in harmonic analysis*in Proceedings of the Edinburgh Mathematical Society
Dendrinos S
(2008)

*Fourier restriction, polynomial curves and a geometric inequality*in Comptes Rendus Mathematique
Dendrinos S
(2009)

*Universal*in Journal of Functional Analysis
Folch-Gabayet M
(2008)

*Singular integral operators associated to curves with rational components*in Transactions of the American Mathematical Society
Jones R
(2008)

*Strong variational and jump inequalities in harmonic analysis*in Transactions of the American Mathematical Society
LAGHI N
(2008)

*A note on restricted X-ray transforms*in Mathematical Proceedings of the Cambridge Philosophical Society
Oberlin R
(2012)

*A variation norm Carleson theorem*in Journal of the European Mathematical Society