We introduce a class of pseudodifferential operators in the anisotropic setting induced by an expansive dilation A which generalizes the classical isotropic class Smγ,δ of inhomogeneous symbols. We extend a well-known L 2-boundedness result to the anisotropic class S0δ,δ(A), 0 ≤ δ < 1. As a consequence, we deduce that operators with symbols in the anisotropic class S01,0(A) are bounded on L p spaces, 1 < p < ∞.
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The final publication is available at Springer via http://dx.doi.org/10.1007/s13348-011-0056-6
Bényi, Árpád and Bownik, Marcin, "Anisotropic Classes of Inhomogeneous Pseudodifferential Symbols" (2013). Mathematics. Paper 45.