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陆善镇
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 122, Number 2, October 1994,-0001,():
-1年11月30日
In this paper we study the bounded property of the Rice means for the cigcnfunction expansio~ foe elliptic operators on the Hardy spaces. Our result generalizes the classical result due to Sjolin and Stein-Taibleson-Weiss on the Boehner-Riesz means.
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【期刊论文】The Continuity of Commutators on Herz-Type Spaces
陆善镇, SHANZHEN LU & DACHUN YANG
,-0001,():
-1年11月30日
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【期刊论文】STRONG SUMMABILITY OF BOCHNER-RIESZ SPHERICAL MEANS
陆善镇, Lu SHANZHEN (陆善镇)
SCIENTIA SINICA (Series A), 1987, XXXⅢ (11): 26~38,-0001,():
-1年11月30日
In this paper, we investigate the strong summability of multiple Fourier series by the Bochner-Riesz spherical means at criticnl index. We prove that the localization theorem of the strosng summability holds for any posityve degree, that is, if f(x) EL(Qn) and f(x)=0(1x-x01), then lim R-∞ 1/R R0|S #-1/2(f; x0)|qdu=0 (for any q>0). We also give certain results on the strong summability which improves Boehner-Ohand sekharan's theorem.
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【期刊论文】Spaces Generated by Smooth Blocks
陆善镇, Shanzhen Lu and Shiming Wang
Constr. Approx. (1992) 8: 331-341,-0001,():
-1年11月30日
A new kind of funcion space generated by somooth blocks is introduced. The new spaces are used to investigate the relation between the smoothness imposed on blocks nad the rate of convergence of the Bochner-Riesz eans at the critical index.
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【期刊论文】On the Almost Everywhere Convergence of Boehner-Riesz Means of Multlple Fourier Series
陆善镇, Lu Shan-zhen, Mitchell H. Taibleson (*), and Guido Weiss (*)
,-0001,():
-1年11月30日
In a recent paper [6] the last two authors of this article introduced a class of function spaces associated with the one-dimensional torus T. They showed that the Fourier series of each function f that belongs to one of these spaces converges to f (x) a.e. Moreover, they indicated that the motion of entropy is closely related to the study of these spaces. These features are not restricted to the one-dimenslonal case. In this paper, in fact, we show how these ideas can be used to study the convergence of Bochner-Riesz means of multiple Fourier series at the "critical index".
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