Abstract
In this note we extend the results in [1] to high dimensions. Let f∈Hp (Tn), 0<p<1, n≥1 andσ δ, f denote the Riesz means of f at the critical index δ=n/p−(n+1)/2. We have the following estimate:
were 0<s≤2 and\(K_s (f,t)_{H^p (T^n )} \), is the K-functional in Hp(Tn).
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References
Chen Guoliang, Jiang Yinsheng and Lu Shanzhen, Strong Approximation of Riesz Means at Critical Index onH p(T)(0<p≤1), Approx. Theory & its Appl., 5(1989), No. 2, 39–49.
Jiang Yinsheng, Liu Heping and Lu Shanzhen, Some Properties of Elliptic Riesz Means at Critical Index onH p(T n), Approx. Theory & its Appl., 6(1990), No. 2, 28–37.
Liu Zhixing, Fourier Multipliers on RealH p(T n) and its Applications, Preprint.
Liu Zhixin, Doctor Dissertation, Beijing Normal University.
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Heping, L., Zhixin, L. & Shanzhen, L. Strong mean approximation on HP(Tn) for the Riesz means at the critical index. Approx. Theory & its Appl. 6, 1–5 (1990). https://doi.org/10.1007/BF02836092
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DOI: https://doi.org/10.1007/BF02836092