m-Microlocal elliptic pseudodifferential operators acting on $L^p_{\rm   loc}(\Omega)$
  In the first part of the paper the authors study the minimal and maximal extension of a class of weighted pseudodifferential operators in the Fr\'echet space $L^p_{\rm loc}(\Omega)$. In the second one non homogeneous microlocal properties are introduced and propagation of Sobolev singularities for solutions to (pseudo)differential equations is given. For both the arguments actual examples are provided. 
Gianluca Garello, Alessandro Morando
math.AP