ACTA issues

Pointwise convergence of Ces?ro and Riesz means on certain function spaces

Shuichi Sato

Acta Sci. Math. (Szeged) 80:1-2(2014), 129-139

Abstract. We consider a function space $\mathscr{QA}$ on the unit sphere of ${\msbm R}^3$, which contains $ L\log L\log\log \log L$, and prove the spherical harmonics expansions of functions in $\mathscr{QA}$ are summable a.e. with respect to the Ces?ro 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 ${\msbm R}^d$, $d\geq2$.

DOI: 10.14232/actasm-012-287-8

AMS Subject Classification (1991): 42C10, 42B08

Keyword(s): spherical harmonics expansion, Ces?ro means, Bochner--Riesz means

Received May 21, 2012, and in revised form September 17, 2012. (Registered under 37/2012.)