TY - JOUR T1 - L^p-regularity for a Class of Pseudodifferential Operators in R^n JO - Journal of Partial Differential Equations VL - 3 SP - 241 EP - 262 PY - 2005 DA - 2005/08 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5360.html KW - Pseudo-differential operators KW - L^p boundedness KW - global hypoellipticity AB -

We study here a class of pseudodifferential operators with weighted symbols of Shubin type. First, we develop the basic elements of the pseudodifferential calculus for these operators, proving in particular a result of L^p-boundedness. Then we derive regularity results in the frame of suitably defined functional spaces of Sobolev type.