Pointwise convergence of Cesàro and Riesz means on certain function spaces | Zendy

Shūichi Satō | Zendy

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Pointwise convergence of Cesàro and Riesz means on certain function spaces

Author(s) -

Shūichi Satō

Publication year - 2014

Publication title -

acta scientiarum mathematicarum

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.386

H-Index - 15

eISSN - 0324-5462

pISSN - 0001-6969

DOI - 10.14232/actasm-012-287-8

Subject(s) - pointwise convergence , mathematics , pointwise , convergence (economics) , pure mathematics , mathematical analysis , computer science , approx , economics , economic growth , operating system

We consider a function space QA on the unit sphere of R 3 , which contains LlogLlogloglogL, and prove the spherical harmonics expansions of functions in QA are summable a.e. with respect to the Cesaro 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 R d , d 2.

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