Almost everywhere divergence of spherical harmonic expansions and equivalence of summation methods
Xianghong Chen
Sun Yat-sen University, Guangzhou, ChinaDashan Fan
University of Wisconsin–Milwaukee, USAJuan Zhang
Beijing Forestry University, China
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Abstract
We show that there exists an integrable function on the -sphere , whose Cesàro means with respect to the spherical harmonic expansion diverge unboundedly almost everywhere. This extends results of Stein (1961) for flat tori and complements the work of Taibleson (1985) for spheres. We also study relations among Cesàro, Riesz, and Bochner–Riesz means.
Cite this article
Xianghong Chen, Dashan Fan, Juan Zhang, Almost everywhere divergence of spherical harmonic expansions and equivalence of summation methods. Rev. Mat. Iberoam. 36 (2020), no. 4, pp. 1133–1148
DOI 10.4171/RMI/1161