Abstract
In this paper we consider\(\mathop {\lim }\limits_{x \to \infty } B_k^a (f,x_0 )\), in one case that fx 0 (t) is a ΛBMV function on [0, ∞], and in another case thatfεL 1 m-1(Rn) and\(\frac{{\partial ^k f}}{{\partial x^k }} \in BV(R^n )\) when |k|=m−1 and f(x)=0 when |x−x0|<δ for some δ>0. Our theormes improve the results of Pan Wenjie ([1]).
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References
Pan Wenjie, On the Localization and Convergence of Multiple Fourier Lntegrals by Spherical Means, Scientia Sinica, 25:4, (1982), 346–362.
Lu Shanzhen and Wang Kunyang, Bochner-Riesz Means, Peking Normal University Press, 1986.
Shi Xianliang, OnΛBMV Function with Some Application to Theory of Fourier Series, Scientia Sinica, 28:2, (1985), 147–158.
Giusti, E., Minimal Surfaces and Function of Bounder Variation, Bosto: Birkhauser, 1984.
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Maohe, Y. On the localization and convergence of multiple Fourier integral by Bochner-Riesz means. Approx. Theory & its Appl. 9, 37–49 (1993). https://doi.org/10.1007/BF02836269
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DOI: https://doi.org/10.1007/BF02836269