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Coriasco","submitted_at":"2012-10-02T07:56:12Z","abstract_excerpt":"We consider certain anisotropic translation invariant pseudodifferential operators, belonging to a class denoted by $\\mathrm{op}(\\mathcal{M}^{\\lambda}_{\\psi})$, where $\\lambda$ and $\\psi=(\\psi_1,\\dots,\\psi_n)$ are the \"order\" and \"weight\" functions, defined on $\\mathbb{R}^n$, for the corresponding space of symbols. We prove that the boundedness of a suitable function $F_p\\colon\\mathbb{R}^n\\to[0,+\\infty)$, $1<p<\\infty$, associated with $\\lambda$ and $\\psi$, is necessary to let every element of $\\mathrm{op}(\\mathcal{M}^{\\lambda}_{\\psi})$ be a $L^p(\\mathbb{R}^n)$-multiplier. 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