Abstract
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.
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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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Chen, J., Fan, D. & Zhao, F. On the Rate of Almost Everywhere Convergence of Combinations and Multivariate Averages. Potential Anal 51, 397–423 (2019). https://doi.org/10.1007/s11118-018-9716-4
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DOI: https://doi.org/10.1007/s11118-018-9716-4