Let p∈（0, 1], q∈（0, ∞] and A be a general expansive matrix on Rn. Let HAp,q （Rn） be the anisotropic Hardy-Lorentz spaces associated with A defined via the non-tangential grand maximal function. In this article,...Let p∈（0, 1], q∈（0, ∞] and A be a general expansive matrix on Rn. Let HAp,q （Rn） be the anisotropic Hardy-Lorentz spaces associated with A defined via the non-tangential grand maximal function. In this article, the authors characterize HAp,q（Rn） in terms of the Lusin-area function, the Littlewood-Paley g-function or the Littlewood-Paley gλ＊-function via first establishing an anisotropic Fefferman-Stein vector-valued inequality in the Lorentz space Lp,q（Rn）. All these characterizations are new even for the classical isotropic Hardy-Lorentz spaces on Rn. Moreover, the range of λ in the gλ＊-function characterization of HAp,q （Rn） coincides with the best known one in the classical Hardy space Hp（Rn） or in the anisotropic Hardy space HAp （Rn）.展开更多
非适应性分组测试算法non-adaptive group testing(NGT)有着广泛的应用,构作检错和纠错能力强的d-disjunct矩阵、(d,e)-disjunct矩阵是非适应性分组测试算法non-adaptive group testing(NGT)的重要内容之一.作者在文献[6]构作了n维射影...非适应性分组测试算法non-adaptive group testing(NGT)有着广泛的应用,构作检错和纠错能力强的d-disjunct矩阵、(d,e)-disjunct矩阵是非适应性分组测试算法non-adaptive group testing(NGT)的重要内容之一.作者在文献[6]构作了n维射影几何上d-disjunct矩阵M,给出了d的估值,从另一个角度证明了d-disjunct矩阵M并分析了它的检错能力.展开更多
The current attempt is aimed to extend previous results, concerning the explicit expression of the arithmetic mean standard deviation distribution, to the general case of the weighted mean standard deviation distribut...The current attempt is aimed to extend previous results, concerning the explicit expression of the arithmetic mean standard deviation distribution, to the general case of the weighted mean standard deviation distribution. To this respect, the integration domain is expressed in canonical form after a change of reference frame in the n-space, which is recognized as an infinitely thin n-cylindrical corona where the axis coincides with a coordinate axis and the orthogonal section is an infinitely thin, homotetic (n-1)-elliptical corona. The semiaxes are formulated in two different ways, namely in terms of (1) eigenvalues, via the eigenvalue equation, and (2) leading principal minors of the matrix of a quadratic form, via the Jacobi formulae. The distribution and related parameters have the same formal expression with respect to their counterparts in the special case where the weighted mean coincides with the arithmetic mean. The reduction of some results to ordinary geometry is also considered.展开更多
基金supported by the National Natural Science Foundation of China(11571039 and 11671185)supported by the National Natural Science Foundation of China(11471042)
文摘Let p∈（0, 1], q∈（0, ∞] and A be a general expansive matrix on Rn. Let HAp,q （Rn） be the anisotropic Hardy-Lorentz spaces associated with A defined via the non-tangential grand maximal function. In this article, the authors characterize HAp,q（Rn） in terms of the Lusin-area function, the Littlewood-Paley g-function or the Littlewood-Paley gλ＊-function via first establishing an anisotropic Fefferman-Stein vector-valued inequality in the Lorentz space Lp,q（Rn）. All these characterizations are new even for the classical isotropic Hardy-Lorentz spaces on Rn. Moreover, the range of λ in the gλ＊-function characterization of HAp,q （Rn） coincides with the best known one in the classical Hardy space Hp（Rn） or in the anisotropic Hardy space HAp （Rn）.
文摘非适应性分组测试算法non-adaptive group testing(NGT)有着广泛的应用,构作检错和纠错能力强的d-disjunct矩阵、(d,e)-disjunct矩阵是非适应性分组测试算法non-adaptive group testing(NGT)的重要内容之一.作者在文献[6]构作了n维射影几何上d-disjunct矩阵M,给出了d的估值,从另一个角度证明了d-disjunct矩阵M并分析了它的检错能力.
文摘The current attempt is aimed to extend previous results, concerning the explicit expression of the arithmetic mean standard deviation distribution, to the general case of the weighted mean standard deviation distribution. To this respect, the integration domain is expressed in canonical form after a change of reference frame in the n-space, which is recognized as an infinitely thin n-cylindrical corona where the axis coincides with a coordinate axis and the orthogonal section is an infinitely thin, homotetic (n-1)-elliptical corona. The semiaxes are formulated in two different ways, namely in terms of (1) eigenvalues, via the eigenvalue equation, and (2) leading principal minors of the matrix of a quadratic form, via the Jacobi formulae. The distribution and related parameters have the same formal expression with respect to their counterparts in the special case where the weighted mean coincides with the arithmetic mean. The reduction of some results to ordinary geometry is also considered.
