Abstract
In this paper it has been considered convergence and approximation for functions in Sobolev spaces\(L_m^l (\mathbb{R}^n )\) by Bochner-Riesz means below the critical index. A theorem that of precise approximation orders on set of total measure has been proved.
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References
Bochner, S., Summation of Multiple Fourier Series by Spherical Means, Trans. Amer. Math. Soc., 40(1936), 175–207.
Pan, W. J., On Localization and Convergence of Riesz means of Multiple Fourier Integrals, Scientia Sinnica(A), 1981, 11:1310–1321 (in Chinese).
Stein, E.M., Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Princeton. 1971.
Stein, E.M., & Weiss, G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, 1971.
Watson, G.N., Theory of Bessel Functions, Cambridge Univ. Press, 1952.
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Shiming, W. Approximation on set of total measure of Bochner-Riesz means below the critical index. Approx. Theory & its Appl. 8, 75–86 (1992). https://doi.org/10.1007/BF02907594
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DOI: https://doi.org/10.1007/BF02907594