In this paper, we prove that the control function of the dilatation function of Beurling-Ahlfors extension is convex. Using the quasi-symmetric function ρ, we get a relatively sharp estimate of the dilatation functio...In this paper, we prove that the control function of the dilatation function of Beurling-Ahlfors extension is convex. Using the quasi-symmetric function ρ, we get a relatively sharp estimate of the dilatation function: D(x,y)≤ 17/32 (ρ(x, y) + 1) (ρ(x + y/2, y/2) +ρ(x - y/2, y/2) +2) , which improves the results before. We also show that the above result is asymptotically precise.展开更多
The Beurling-Ahlfors’ extension is studied under relatively general conditions and its dilatation fonction is estimated. Particularly, the classic Deurling -Ahlfors’ theorem can be obtained under the M-condition.
Objective To compare the different effects of endothelia progenitor cells （ EPCs ） or basic fibroblast growth factor （b-FGF） intromyocardial infusion on cardiac function and neovascularization for dilated cardiomy...Objective To compare the different effects of endothelia progenitor cells （ EPCs ） or basic fibroblast growth factor （b-FGF） intromyocardial infusion on cardiac function and neovascularization for dilated cardiomyopathy（ DCM） rats. Methods Fifty adult female rats received inguinal subcutaneous injections of isoproterenol （ISO, 250 mg/kg） for induction of DCM. Four weeks later, the model rats were randomly divided into EPCs group, b-FGF group and control group. The 2×106 EPCs （ resolved in 100 μL PBS） , 100 μL b-FGF （ lO0 μg/mL ） and 100 μL PBS were evenly transplanted into the myocardium of EPCs group, b-FGF group and control group, respectively. Three months later, echocardiographic examination and regional myocardial blood flow （RMBF） measurement were performed. EPCs were traced by fluorescence in situ hybridization （FISH）. The protein and mRNA expression of b-FGF in each group was measured by ELISA assay and reverse transcription-polymerase chain reaction （ RT-PCR ） . Results Three months after transplantation, sry positive cells were detected only in EPCs group. The cardiac function as well as RMBF was significantly improved in EPCs group compared with b-FGF group or control group. There was higher capillary density in EPCs group. The protein and mRNA expression of b-FGF was stronger than b-FGF group and control group. Conclusion Transplantation of EPCs can improve cardiac function, induce neovascularization and increase RMBF for DCM rats. The treatment with EPCs has better effect than administration of b-FGF alone.展开更多
An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We exten...An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We extend their results to the dilation matrix cases in two aspects. We first show that the periodization of any wavelet frame constructed by the unitary extension principle formulated by Ron and Shen is still a periodic wavelet frame under weaker conditions than that given by Zhang and Saito, and then prove that the periodization of those generated by the mixed extension principle is also a periodic wavelet frame if the scaling functions have compact supports.展开更多
Let A :=(A_1, A_2) be a pair of expansive dilations and φ : R^n×R^m×[0, ∞) → [0, ∞) an anisotropic product Musielak-Orlicz function. In this article, we introduce the anisotropic product Musielak-Orlicz ...Let A :=(A_1, A_2) be a pair of expansive dilations and φ : R^n×R^m×[0, ∞) → [0, ∞) an anisotropic product Musielak-Orlicz function. In this article, we introduce the anisotropic product Musielak-Orlicz Hardy space H~φ_A(R^n× R^m) via the anisotropic Lusin-area function and establish its atomic characterization, the g-function characterization, the g_λ~*-function characterization and the discrete wavelet characterization via first giving out an anisotropic product Peetre inequality of Musielak-Orlicz type. Moreover, we prove that finite atomic decomposition norm on a dense subspace of H~φ_A(R^n× R^m) is equivalent to the standard infinite atomic decomposition norm. As an application, we show that, for a given admissible triplet(φ, q, s), if T is a sublinear operator and maps all(φ, q, s)-atoms into uniformly bounded elements of some quasi-Banach spaces B, then T uniquely extends to a bounded sublinear operator from H~φ_A(R^n× R^m) to B. Another application is that we obtain the boundedness of anisotropic product singular integral operators from H~φ_A(R^n× R^m) to L~φ(R^n× R^m)and from H~φ_A(R^n×R^m) to itself, whose kernels are adapted to the action of A. The results of this article essentially extend the existing results for weighted product Hardy spaces on R^n× R^m and are new even for classical product Orlicz-Hardy spaces.展开更多
基金Supported by the National Natural Science Foundation of China(10271077)Supported by the Educational Department of Zhejiang Province Natural Science Project(20030768)
文摘In this paper, we prove that the control function of the dilatation function of Beurling-Ahlfors extension is convex. Using the quasi-symmetric function ρ, we get a relatively sharp estimate of the dilatation function: D(x,y)≤ 17/32 (ρ(x, y) + 1) (ρ(x + y/2, y/2) +ρ(x - y/2, y/2) +2) , which improves the results before. We also show that the above result is asymptotically precise.
文摘The Beurling-Ahlfors’ extension is studied under relatively general conditions and its dilatation fonction is estimated. Particularly, the classic Deurling -Ahlfors’ theorem can be obtained under the M-condition.
文摘Objective To compare the different effects of endothelia progenitor cells （ EPCs ） or basic fibroblast growth factor （b-FGF） intromyocardial infusion on cardiac function and neovascularization for dilated cardiomyopathy（ DCM） rats. Methods Fifty adult female rats received inguinal subcutaneous injections of isoproterenol （ISO, 250 mg/kg） for induction of DCM. Four weeks later, the model rats were randomly divided into EPCs group, b-FGF group and control group. The 2×106 EPCs （ resolved in 100 μL PBS） , 100 μL b-FGF （ lO0 μg/mL ） and 100 μL PBS were evenly transplanted into the myocardium of EPCs group, b-FGF group and control group, respectively. Three months later, echocardiographic examination and regional myocardial blood flow （RMBF） measurement were performed. EPCs were traced by fluorescence in situ hybridization （FISH）. The protein and mRNA expression of b-FGF in each group was measured by ELISA assay and reverse transcription-polymerase chain reaction （ RT-PCR ） . Results Three months after transplantation, sry positive cells were detected only in EPCs group. The cardiac function as well as RMBF was significantly improved in EPCs group compared with b-FGF group or control group. There was higher capillary density in EPCs group. The protein and mRNA expression of b-FGF was stronger than b-FGF group and control group. Conclusion Transplantation of EPCs can improve cardiac function, induce neovascularization and increase RMBF for DCM rats. The treatment with EPCs has better effect than administration of b-FGF alone.
基金Acknowledgements The authors express their gratitude to the anonymous referees for their kind suggestions and useful comments on the original manuscript, which resulted in this final version. This work was supported by the National Natural Science Foundation of China （No. 61071189）, the Natural Science Foundation for the Education Department of Henan Province of China （No. 13A110072）, and the Natural Science Foundation of Henan University （No. 2011YBZR001）.
文摘An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We extend their results to the dilation matrix cases in two aspects. We first show that the periodization of any wavelet frame constructed by the unitary extension principle formulated by Ron and Shen is still a periodic wavelet frame under weaker conditions than that given by Zhang and Saito, and then prove that the periodization of those generated by the mixed extension principle is also a periodic wavelet frame if the scaling functions have compact supports.
基金supported by National Natural Science Foundation of China (Grant Nos. 11671414, 11271091, 11471040, 11461065, 11661075, 11571039 and 11671185)
文摘Let A :=(A_1, A_2) be a pair of expansive dilations and φ : R^n×R^m×[0, ∞) → [0, ∞) an anisotropic product Musielak-Orlicz function. In this article, we introduce the anisotropic product Musielak-Orlicz Hardy space H~φ_A(R^n× R^m) via the anisotropic Lusin-area function and establish its atomic characterization, the g-function characterization, the g_λ~*-function characterization and the discrete wavelet characterization via first giving out an anisotropic product Peetre inequality of Musielak-Orlicz type. Moreover, we prove that finite atomic decomposition norm on a dense subspace of H~φ_A(R^n× R^m) is equivalent to the standard infinite atomic decomposition norm. As an application, we show that, for a given admissible triplet(φ, q, s), if T is a sublinear operator and maps all(φ, q, s)-atoms into uniformly bounded elements of some quasi-Banach spaces B, then T uniquely extends to a bounded sublinear operator from H~φ_A(R^n× R^m) to B. Another application is that we obtain the boundedness of anisotropic product singular integral operators from H~φ_A(R^n× R^m) to L~φ(R^n× R^m)and from H~φ_A(R^n×R^m) to itself, whose kernels are adapted to the action of A. The results of this article essentially extend the existing results for weighted product Hardy spaces on R^n× R^m and are new even for classical product Orlicz-Hardy spaces.
