Anisotropic Classes of Inhomogeneous Pseudodifferential Symbols

We introduce a class of pseudodifferential operators in the anisotropic setting induced by an expansive dilation A which generalizes the classical isotropic class S γ,δ of inhomogeneous symbols. We extend a well-known L -boundedness result to the anisotropic class S δ,δ(A), 0 ≤ δ < 1. As a consequence, we deduce that operators with symbols in the anisotropic class S 1,0(A) are bounded on L p spaces, 1 < p <∞.