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arXiv · 2609.14023

Spherical harmonics with maximal Lp norm growth

Xiaolong Han
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Abstract

In this paper, we show that for every p>2, there is an orthonormal basis of spherical harmonics on Sn with n>=2 which achieves the maximal Lp norm growth. More precisely, one basis achieves this growth for all p<=2(n+1)/(n-1), and another for all p>=2(n+1)/(n-1). This extends the results in Han (arXiv:1404.5016) to all dimensions and all p>2, and improves the positive density subsequence there to a whole basis.

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Xiaolong Han. 2026-09-19. Spherical harmonics with maximal Lp norm growth. https://arxiv.org/abs/2609.14023

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