Rubens Longhi (UP)
We aim at extending the classical notion of smooth wavefront set employing the Radon transform in order to capture different degrees of lack of \(\mathcal{F}\)-regularity of a distribution \(u\) around a certain co-direction \(\xi\), e.g. for \(\mathcal{F}=\) Sobolev or Hölder spaces on \(\mathbb{R}\). In order to extend the usual smooth microlocal regularity theorem to this setting, it is technically necessary to assume that the space of regularity \(\mathcal{F}\) is invariant under the action of a certain Fourier Integral Operator of order zero, obtained by inverting the Radon transform. In the talk we will investigate whether such operator can be reduced to a pseudodifferential one, weakening the assumptions on \(\mathcal{F}\).
