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 suitably defined family of weighted Sobolev spaces. Results about L^p-regularity for multi-quasi-elliptic pseudodifferential operators are also given.
L^p-bounded pseudodifferential operators and regularity for multi-quasi-elliptic equations
GARELLO, Gianluca;
2005-01-01
Abstract
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 suitably defined family of weighted Sobolev spaces. Results about L^p-regularity for multi-quasi-elliptic pseudodifferential operators are also given.
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