Besov Wavefront Set

Abstract

We develop a notion of wavefront set aimed at characterizing in Fourier space the directions along which a distribution behaves or not as an element of a specific Besov space. Subsequently we prove an alternative, albeit equivalent characterization of such wavefront set using the language of pseudo-differential operators. Both formulations are used to prove the main underlying structural properties. Among these we highlight the individuation of a sufficient criterion to multiply distributions with a prescribed Besov wavefront set which encompasses and generalizes the classical Young's theorem. At last, as an application of this new framework we prove a theorem of propagation of singularities for a large class of hyperbolic operators.

24 pages

References in corpus (3)

• Reconstruction Theorem for Germs of Distributions on Smooth Manifolds
• An Algebraic and Microlocal Approach to the Stochastic Non-linear Schrödinger Equation
• On a Microlocal Version of Young's Product Theorem