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Anisotropic Classes Of Inhomogeneous Pseudodifferential Symbols, Árpád Bényi, Marcin Bownik

Mathematics Faculty Publications

We introduce a class of pseudodifferential operators in the anisotropic setting induced by an expansive dilation A which generalizes the classical isotropic class S^m_γ,δ of inhomogeneous symbols. We extend a well-known L ²-boundedness result to the anisotropic class S⁰_δ,_δ(A), 0 ≤ δ < 1. As a consequence, we deduce that operators with symbols in the anisotropic class S⁰_1,0(A) are bounded on L ^p spaces, 1 < p < ∞.