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 ???,? of inhomogeneous symbols. We extend a well-known L 2-boundedness result to the anisotropic class ?0?,?(?) , 0 ≤ δ < 1. As a consequence, we deduce that operators with symbols in the anisotropic class ?01,0(?) are bounded on L p spaces, 1 < p < ∞.