Anisotropic classes of inhomogeneous pseudodifferential symbols
Tóm tắt
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 < ∞.
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