Abstract
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 \(H^{p}\left( \mathbb {M}\right) \), \(0<p\le 1.\)
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Acknowledgements
The research was supported by National Natural Science Foundation of China (Grant Nos. 11471288, 11971295), Natural Science Foundation of Shanghai (No. 19ZR1417600), and Natural Science Foundation of Zhejiang (No. LQ20A010003).
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Fan, D., Zhao, J. Bochner–Riesz Means and K-Functional on Compact Manifolds. Results Math 76, 140 (2021). https://doi.org/10.1007/s00025-021-01449-8
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DOI: https://doi.org/10.1007/s00025-021-01449-8