On the Rate of Almost Everywhere Convergence of Combinations and Multivariate Averages

  • Jiecheng Chen
  • Dashan Fan
  • Fayou Zhao


The main purpose of this paper is to establish results concerning the rate of almost everywhere convergence of the combinations and multivariate averages on Sobolev type spaces on the Euclidean space \(\mathbb {R}^{n}\). The saturation of convergence is also obtained. As an application, the corresponding results can be extended to the n-torus \(\mathbb {T}^{n}\), by using some transference theorems.


Combination and multivariate average Multipliers Almost everywhere Saturation Fourier series 

Mathematics Subject Classification (2010)

41A25 41A63 42B15 


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The research was supported by National Natural Science Foundation of China (Grant Nos. 11671363, 11601456) and China Scholarship Council (Grant No. 201406895019).


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang Normal UniversityJinhuaPeople’s Republic of China
  2. 2.Department of Mathematical SciencesUniversity of Wisconsin-MilwaukeeMilwaukeeUSA
  3. 3.Department of MathematicsShanghai UniversityShanghaiPeople’s Republic of China

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