**SMS scnews item created by Daniel Daners at Sun 3 Feb 2019 1849**

Type: Seminar

Distribution: World

Expiry: 11 Feb 2019

**Calendar1: 11 Feb 2019 1400-1500**

**CalLoc1: AGR Carslaw 829**

CalTitle1: PDESeminar: Spaces of functions invariant under Fourier integral operators of order zero (Hassell)

Auth: daners@d27-99-38-95.bla1.nsw.optusnet.com.au (ddan2237) in SMS-WASM

### PDE Seminar

# Spaces of functions invariant under Fourier integral operators of order zero

### Hassell

Andrew Hassell

Australian National University, Canberra, Australia

Mon 11th Feb 2019, 2-3pm, Carslaw Room 829 (AGR)

## Abstract

It was proved by Seeger, Sogge and Stein that Fourier Integral operators (FIOs) in
$n$ dimensions map
the Hardy space ${H}^{1}$
into ${L}^{1}$
provided they have sufficiently negative order, that is, no bigger than
$-\left(n-1\right)\u22152$. I will
describe joint work with Pierre Portal and Jan Rozendaal, based on earlier work
of Hart Smith, on constructing Hardy-type spaces that are invariant under all
FIOs (associated to a canonical graph) of order zero. We hope to use these
spaces in future work to solve wave equations with rough coefficients.it was
proved by Seeger, Sogge and Stein that Fourier Integral operators (FIOs) in
$n$ dimensions map
the Hardy space ${H}^{1}$
into ${L}^{1}$
provided they have sufficiently negative order, that is, no bigger than
$-\left(n-1\right)\u22152$.

I will describe joint work with Pierre Portal and Jan Rozendaal, based on
earlier work of Hart Smith, on constructing Hardy-type spaces that are invariant
under all FIOs (associated to a canonical graph) of order zero. We hope to use
these spaces in future work to solve wave equations with rough coefficients.

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