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In the first part of the paper the authors study the minimal and maximalextension of a class of weighted pseudodifferential operators in the Fr\'echetspace $L^p_{\rm loc}(\Omega)$. In the second one non homogeneous microlocalproperties are introduced and propagation of Sobolev singularities forsolutions to (pseudo)differential equations is given. For both the argumentsactual examples are provided.

m-Microlocal elliptic pseudodifferential operators acting on $L^p_{\rm loc}(\Omega)$