The main aim of this article is to prove that the maximal operator σ^k＊ of the Marcinkiewicz-Fejer means of the two-dimensional Fourier series with respect to Walsh- Kaczmarz system is bounded from the Hardy space H...The main aim of this article is to prove that the maximal operator σ^k＊ of the Marcinkiewicz-Fejer means of the two-dimensional Fourier series with respect to Walsh- Kaczmarz system is bounded from the Hardy space H2/3 to the space weak-L2/3.展开更多
Nodal, a member of the transforming growth factor β （TGF-β） superfamily, has been shown to play a role in mesendoderm induction and gastrulation movements. The activity of Nodal signaling can be modulated by micro...Nodal, a member of the transforming growth factor β （TGF-β） superfamily, has been shown to play a role in mesendoderm induction and gastrulation movements. The activity of Nodal signaling can be modulated by microRNAs （miRNAs） as previously reported, but little is known about which miRNAs are regulated by Nodal during gastrulation. In the present study, we found that the expression of mir206, one of the most abundant miRNAs during zebrafish early embryo development, is regulated by Nodal signaling. Abrogation of Nodal signal activity results in defective convergence and extension （CE） movements, and these cell migration defects can be rescued by supplying an excess of mir206, suggesting that mir206 acts downstream of Nodal signaling to regulate CE movements. Furthermore, in mir206 morphants, the expression of cell adhesion molecule E-cadherin is significantly increased, while the key transcriptional repressor of E-cadherin, snailla, is depressed. Our study uncovers a novel mechanism by which Nodal-regulated mir206 modulates gastrulation movements in connection with the Snail/E-cadherin pathway.展开更多
A covering lemma on the unit sphere is established and then is applied to establish an almost everywhere convergence test of Marcinkiewicz type for the Fourier-Laplace series on the unit sphere which can be stated as ...A covering lemma on the unit sphere is established and then is applied to establish an almost everywhere convergence test of Marcinkiewicz type for the Fourier-Laplace series on the unit sphere which can be stated as follows：Theorem Suppose f ∈ L（En-1）, n≥ 3. If f satisfies the condition1/θ^n-1∫D（x,θ）｜f（y）-f（x）｜dy=O（1/｜logθ｜）,as θ→0＋,at every point x in a set E of positive measure in Σn-1, then the Cesàro means of critical order ,n-2/2 of the Fourier-Laplace series of f converge to f at almost every point x in E.展开更多
基金supported by project TMOP-4.2.2.A-11/1/KONV-2012-0051,Shota Rustaveli National Science Foundation grant no.13/06(Geometry of function spaces,interpolation and embedding theorems)
文摘The main aim of this article is to prove that the maximal operator σ^k＊ of the Marcinkiewicz-Fejer means of the two-dimensional Fourier series with respect to Walsh- Kaczmarz system is bounded from the Hardy space H2/3 to the space weak-L2/3.
基金supported by the grants from the Major Science Programs of China(Nos.2011CBA01101 and 2011CB943904)the National Natural Science Foundation of China(Nos.30971656 and 90919011)
文摘Nodal, a member of the transforming growth factor β （TGF-β） superfamily, has been shown to play a role in mesendoderm induction and gastrulation movements. The activity of Nodal signaling can be modulated by microRNAs （miRNAs） as previously reported, but little is known about which miRNAs are regulated by Nodal during gastrulation. In the present study, we found that the expression of mir206, one of the most abundant miRNAs during zebrafish early embryo development, is regulated by Nodal signaling. Abrogation of Nodal signal activity results in defective convergence and extension （CE） movements, and these cell migration defects can be rescued by supplying an excess of mir206, suggesting that mir206 acts downstream of Nodal signaling to regulate CE movements. Furthermore, in mir206 morphants, the expression of cell adhesion molecule E-cadherin is significantly increased, while the key transcriptional repressor of E-cadherin, snailla, is depressed. Our study uncovers a novel mechanism by which Nodal-regulated mir206 modulates gastrulation movements in connection with the Snail/E-cadherin pathway.
基金supported by the NSF of China,No.10471010the Natural Science Foundation of Tianjin Normal University,52LJ32The Planned Project of the Development Foundation of Science and Technology of Universities in Tianjin
文摘A covering lemma on the unit sphere is established and then is applied to establish an almost everywhere convergence test of Marcinkiewicz type for the Fourier-Laplace series on the unit sphere which can be stated as follows：Theorem Suppose f ∈ L（En-1）, n≥ 3. If f satisfies the condition1/θ^n-1∫D（x,θ）｜f（y）-f（x）｜dy=O（1/｜logθ｜）,as θ→0＋,at every point x in a set E of positive measure in Σn-1, then the Cesàro means of critical order ,n-2/2 of the Fourier-Laplace series of f converge to f at almost every point x in E.
