Abstract
We consider a function space \(\mathscr{QA}\) on the unit sphere of ℝ3, which contains Llog Llog log log L, and prove the spherical harmonics expansions of functions in \(\mathscr{QA}\) are summable a.e. with respect to the Cesàro means of the critical order 1/2. We also prove that a similar result holds for the Bochner- Riesz means of multiple Fourier series of periodic functions on ℝd, d ≥ 2.
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Sato, S. Pointwise convergence of Cesàro and Riesz means on certain function spaces. ActaSci.Math. 80, 129–139 (2014). https://doi.org/10.14232/actasm-012-287-8
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DOI: https://doi.org/10.14232/actasm-012-287-8