Resumen de Anisotropic classes of inhomogeneous pseudodifferential symbols

Arpad Bényi, Marcin Bownik

• 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}_{\gamma, \delta}} of inhomogeneous symbols. We extend a well-known L 2-boundedness result to the anisotropic class {S_{\delta, \delta}^0(A)}, 0 ≤ δ < 1. As a consequence, we deduce that operators with symbols in the anisotropic class {S^0_{1,0}(A)} are bounded on L p spaces, 1 < p < ∞.