We prove a two-sided transference theorem between \(L^{p}\) spherical multipliers on the compact symmetric space U/K and \(L^{p}\) multipliers on the vector space \(i{\mathfrak {p}},\) where the Lie algebra of U has Cartan decomposition \(\mathfrak {k\oplus }i{\mathfrak {p}}\). This generalizes the classic theorem transference theorem of deLeeuw relating multipliers on \( L^{p}(\mathbb {T)}\) and \(L^{p}(\mathbb {R)}\).

中文翻译：

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在紧凑的对称空间上传递球面乘法器

我们证明之间的双面转移定理\（L ^ {P} \）上的紧凑对称空间球形乘法器ú / ķ和\（L ^ {P} \）上的矢量空间乘法器\（ⅰ{\ mathfrak { p}}，\）其中U的李代数具有Cartan分解\（\ mathfrak {k \ oplus} i {\ mathfrak {p}} \）。这将deLeeuw的经典定理转移定理推广到\（L ^ {p}（\ mathbb {T）} \）和\（L ^ {p}（\ mathbb {R）} \）上的乘子。