In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I＊ and Cesàro mean operator σ＊ are bounded from the B-valued martingale Hardy spaces pΣα, Dα,...In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I＊ and Cesàro mean operator σ＊ are bounded from the B-valued martingale Hardy spaces pΣα, Dα, pLα, p H#α, pKr to Lα （0 α ∞）, respectively. The facts show that it depends on the geometrical properties of the Banach space.展开更多
In this paper we prove that the maximal operator I of dyadic derivative is not bounded from the Hardy space H p [0, 1] to the Hardy space H p [0, 1], when 0 〈 p ≤ 1.
The principles of the new maximal operator H＊ we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz L^Xp.q[0,1） to the Lorentz L^Xp.q[0,1） for 1/2〈 p〈∞, 0〈~ q ≤ ∞, where X is any...The principles of the new maximal operator H＊ we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz L^Xp.q[0,1） to the Lorentz L^Xp.q[0,1） for 1/2〈 p〈∞, 0〈~ q ≤ ∞, where X is any Banach space. When the Banach space X has the RN property, the sequence dnHnf converges to f a.e. Meanwhile the convergence in L^Xp norm for 1≤p〈∞ is a consequence of that the family functions K （n∈N） is an approximate identity.展开更多
In this article, the Banach space X and the martingales with values in it are considered. It is shown that the maximal operators of the one-dimensional dyadic derivative of the dyadic integral and Cesaro means are bou...In this article, the Banach space X and the martingales with values in it are considered. It is shown that the maximal operators of the one-dimensional dyadic derivative of the dyadic integral and Cesaro means are bounded from the dyadic Hardy- Lorentz space pH^-ra（X） to Lra（X） when X is isomorphic to a p-uniformly smooth space （1 〈p ≤ 2）. And it is also bounded from Hra（X） to Lra（X） （0 〈 r 〈 ∞,0 〈 a≤oc） when X has Radon-Nikodym property. In addition, some weak-type inequalities are given.展开更多
In [1] the boundedness of one dimensional maximal operator of dyadic derivative is discussed. In this paper, we consider the two-dimensional maximal operator of dyadic derivative on Vilenkin martingale spaces. With th...In [1] the boundedness of one dimensional maximal operator of dyadic derivative is discussed. In this paper, we consider the two-dimensional maximal operator of dyadic derivative on Vilenkin martingale spaces. With the help of countcr-example we prove that the maximal operator is not bounded from the Hardy spacc Hq to the Hardy space Hq for 0 ≤ q ≤1 and is bounded from p∑a, Da to La for some a.展开更多
Since the Leibniz-Newton formula for derivatives cannot be used in local fields, it is important to investigate the new concept of derivatives in Walsh-analysis, or harmonic analysis on local fields. On the basis of i...Since the Leibniz-Newton formula for derivatives cannot be used in local fields, it is important to investigate the new concept of derivatives in Walsh-analysis, or harmonic analysis on local fields. On the basis of idea of derivatives introduced by Butzer, Schipp and Wade, Weisz has proved that the maximal operators of the one-dimensional dyadic derivative and integral are bounded from the dyadic Hardy space Hp,q to Lp,q, of weak type （L1,L1）, and the corresponding maximal operators of the two-dimensional case are of weak type （Hi, L1）. In this paper, we show that these maximal operators are bounded both on the dyadic Hardy spaces Hp and the hybrid Hardy spaces H^#p 0〈p≤1.展开更多
基金supported by the Nation Natural Science Foundation of China(10671147)Wuhan University of Science and Engineering under grant (093877)
文摘In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I＊ and Cesàro mean operator σ＊ are bounded from the B-valued martingale Hardy spaces pΣα, Dα, pLα, p H#α, pKr to Lα （0 α ∞）, respectively. The facts show that it depends on the geometrical properties of the Banach space.
文摘In this paper we prove that the maximal operator I of dyadic derivative is not bounded from the Hardy space H p [0, 1] to the Hardy space H p [0, 1], when 0 〈 p ≤ 1.
基金Supported by the National Natural Science Foundation of China(10671147)
文摘The principles of the new maximal operator H＊ we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz L^Xp.q[0,1） to the Lorentz L^Xp.q[0,1） for 1/2〈 p〈∞, 0〈~ q ≤ ∞, where X is any Banach space. When the Banach space X has the RN property, the sequence dnHnf converges to f a.e. Meanwhile the convergence in L^Xp norm for 1≤p〈∞ is a consequence of that the family functions K （n∈N） is an approximate identity.
基金supported by the National Natural Science Foundation of China (10371093)
文摘In this article, the Banach space X and the martingales with values in it are considered. It is shown that the maximal operators of the one-dimensional dyadic derivative of the dyadic integral and Cesaro means are bounded from the dyadic Hardy- Lorentz space pH^-ra（X） to Lra（X） when X is isomorphic to a p-uniformly smooth space （1 〈p ≤ 2）. And it is also bounded from Hra（X） to Lra（X） （0 〈 r 〈 ∞,0 〈 a≤oc） when X has Radon-Nikodym property. In addition, some weak-type inequalities are given.
基金supported by National Natural Science Foundation of China (11201354)Hubei Province Key Laboratory of Systems Science in Metallurgical Process (Wuhan University of Science and Technology) (Y201121)+3 种基金National Natural Science Foundation of Pre-Research Project (2011XG005)supported by Natural Science Fund of Hubei Province (2010CDB03305)Wuhan Chenguang Program (201150431096)Open Fund of State Key Laboratory of Information Engineeringin Surveying Mapping and Remote Sensing (11R01)
文摘In [1] the boundedness of one dimensional maximal operator of dyadic derivative is discussed. In this paper, we consider the two-dimensional maximal operator of dyadic derivative on Vilenkin martingale spaces. With the help of countcr-example we prove that the maximal operator is not bounded from the Hardy spacc Hq to the Hardy space Hq for 0 ≤ q ≤1 and is bounded from p∑a, Da to La for some a.
基金the Preliminary Research Foundation of National Defense (No,002,2BQ) the Foundation of Fuzhou University (No.0030824649)
文摘Since the Leibniz-Newton formula for derivatives cannot be used in local fields, it is important to investigate the new concept of derivatives in Walsh-analysis, or harmonic analysis on local fields. On the basis of idea of derivatives introduced by Butzer, Schipp and Wade, Weisz has proved that the maximal operators of the one-dimensional dyadic derivative and integral are bounded from the dyadic Hardy space Hp,q to Lp,q, of weak type （L1,L1）, and the corresponding maximal operators of the two-dimensional case are of weak type （Hi, L1）. In this paper, we show that these maximal operators are bounded both on the dyadic Hardy spaces Hp and the hybrid Hardy spaces H^#p 0〈p≤1.
