Spaces of functions invariant under Fourier integral operators of order zero

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 $-\left(n-1\right)∕2$. 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 $-\left(n-1\right)∕2$.

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.