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 pseudodifferential 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.

我们提出了波前集的概念，旨在表征傅立叶空间中分布作为特定贝索夫空间元素或不作为特定贝索夫空间元素的方向。随后，我们使用伪微分算子的语言证明了这种波前集的替代方案，尽管是等效的表征。两种公式都用于证明主要的基础结构特性。其中，我们强调了充分标准的个性化，以将分布与规定的贝索夫波前集相乘，该波前集包含并概括了经典杨氏定理。最后，作为这个新框架的应用，我们证明了一大类双曲算子的奇点传播定理。