On a compact connected manifold \(\mathbb {M}\), we obtain an \(L^{p}\) equivalence relation between the K-functional and the approximation of the Bochner–Riesz multiplier operator, under the sharp condition on its index. When \(\mathbb {M}\) is a compact Lie group, a similar result is obtained between the Bochner–Riesz multiplier operator and the K-functional on the Hardy space \(H^{p}\left( \mathbb {M}\right) \), \(0<p\le 1.\)

中文翻译：

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紧凑流形上的 Bochner-Riesz 均值和 K 泛函

在紧凑连通流形\(\mathbb {M}\) 上，我们获得了 K 泛函与 Bochner-Riesz 乘子算子的近似值之间的\(L^{p}\)等价关系，在尖锐条件下它的索引。当\(\mathbb {M}\)是紧李群时，Bochner-Riesz 乘子算子和Hardy 空间上的K-泛函得到类似的结果\(H^{p}\left( \mathbb { M}\right) \) , \(0<p\le 1.\)