JournalsrmiVol. 36, No. 4pp. 1133–1148

Almost everywhere divergence of spherical harmonic expansions and equivalence of summation methods

  • Xianghong Chen

    Sun Yat-sen University, Guangzhou, China

  • Dashan Fan

    University of Wisconsin–Milwaukee, USA

  • Juan Zhang

    Beijing Forestry University, China
Almost everywhere divergence of spherical harmonic expansions and equivalence of summation methods cover

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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