LP-bounded pseudodifferential operators and regularity for multi-quasi-elliptic equations

Using a classical result of Marcinkiewicz and Lizorkin about the L-p-continuity for Fourier multipliers, the authors study the action of a class of pseudodifferential operators with weighted smooth symbol on a family of weighted Sobolev spaces. Results about L-p-regularity for multi-quasi-elliptic pseudo differential operators are also given.