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Sharp bounds for Hardy type operators on higher-dimensional product spaces

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Frontiers of Mathematics in China 2018年第6期13卷 1341-1353页

作者： qianjun he Xiang LI Dunyan YAN School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049 China

We investigate a class of fractional Hardy type operators $${\mathscr{H}_{{\beta _1},{\beta _2}, \ldots ,{\beta _m}}}$$ ... 详细信息

We investigate a class of fractional Hardy type operators $${\mathscr{H}_{{\beta _1},{\beta _2}, \ldots ,{\beta _m}}}$$ defined on higher-dimensional product spaces $${\mathbb{R}^{{n_1}}} \times {\mathbb{R}^{{n_2}}} \times \cdots \times {\mathbb{R}^{{n_m}}}$$ and use novel methods to obtain their sharp bounds. In particular, we optimize the result due to S. M. Wang, S. Z. Lu, and D. Y. Yan [Sci. China Math., 2012, 55(12): 2469–2480].

关键词： Hardy type operators power weight sharp bounds

Fe-porphyrin:A redox-related biosensor of hydrogen molecule

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Nano Research 2023年第2期16卷 2020-2025页

作者： Zhaokui Jin Penghe Zhao Wanjun Gong Wenjiang Ding qianjun he Center of Hydrogen Science School of Materials Science and EngineeringShanghai Jiao Tong University800 Dongchuan RoadShanghai 200240China School of Biomedical Engineering Health Science CenterShenzhen University1066 Xueyuan RoadShenzhen 518060China

Hydrogen molecule(H_(2))exhibits broad-spectrum but microenvironment-dependent biomedical effects in varied oxidation stress-related diseases,but its molecular mechanism is unclear and its targeting molecule is unknown so ***,we originally reveal that Fe-porphyrin is a H_(2)-targeted *** have demonstrated that the oxidized Fe-porphyrin in both free and protein-confining states can self-catalyze the hydrogenation/reduction by reacting with H_(2)to catalytically scavenge∙OH,and can also catalytically hydrogenate to reduce CO_(2)into CO in the hypoxic microenvironment of in vitro simulation and in vivo tumor,confirming that Fe-porphyrin is a redox-related biosensor of H_(2)and H_(2)is an upstream signaling molecule of *** discoveries are favorable for deep understanding and exploration of profound biomedical effects of H2,and helpful for development of innovative drugs and hydrogen energy/agricultural materials.

关键词： hydrogen molecule molecular mechanism molecular target hydrogen medicine porphyrin catalysis carbon monoxide

Equivalence of operator norm for Hardy-Littlewood maximal operators and their truncated operators on Morrey spaces

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Frontiers of Mathematics in China 2020年第1期15卷 215-223页

作者： Xingsong ZHANG Mingquan WEI Dunyan YAN qianjun he School of Mathematics University of Chinese Academy of SciencesBeijing 100049China School of Mathematics and Statistics Xinyang Normal UniversityXinyang 464000China School of Applied Science Beijing Information Science and Technology UniversityBeijing 100192China

We will prove that for 1he central Morrey norm of the truncated centered Hardy-Littlewood maximal operator Mcγequals that of the centered Hardy-Littlewood maximal operator for all 0hen p=1 and 0he weak central Morrey norm of the truncated centered Hardy-Littlewood maximal operator Mcγequals that of the centered Hardy-Littlewood maximal operator for all 0he same results are true for the truncated uncentered Hardy-Littlewood maximal *** work extends the previous results of Lebesgue spaces to Morrey spaces.

关键词： Hardy-Littlewood maximal function truncated Hardy-Littlewood maximal function Morrey norms weak Morrey norms

BOUNDEDNESS OF MULTILINEAR LITTLEWOOD-PALEY OPERATORS ON AMALGAM-CAMPANATO SPACES

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Acta Mathematica Scientia 2020年第1期40卷 272-292页

作者： Xiang LI qianjun he Dunyan YAN School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China School of Applied Science Beijing Information Science and Technology UniversityBeijing 100192China

In this paper,we consider the boundedness of multilinear Littlewood-Paley operators which include multilinear g-function,multilinear Lusin's area integral and multilinear Littlewood-Paley g^*λ-***,norm inequalities o... 详细信息

关键词： multilinear Littlewood-Paley g-function multilinear g^*λ-function AmalgamCampanato spaces

BOUNDS FOR MULTILINEAR OPERATORS UNDER AN INTEGRAL TYPE CONDITION ON MORREY SPACES

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Acta Mathematica Scientia 2022年第3期42卷 1191-1208页

作者： qianjun he Xinfeng WU Dunyan YAN School of Applied Science Beijing Information Science and Technology UniversityBeijing 100192China Department of Mathematics China University Mining&Technology(Beijing)Beijing 100083China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper,we study a boundedness property of the Adams type for multilinear fractional integral operators with the multilinear L^(r′,α)-Hörmander condition and their commutators with vector valued BMO functions on a Morrey space and a predual Morrey ***,we give an endpoint estimate for multilinear fractional integral *** an application,we obtain the boundedness of multilinear Fourier multipliers with limited Sobolev regularity on a Morrey space.

关键词： Multilinear fractional integral L^(r′,α)-Höormander condition commutators BMO spaces Morrey spaces multilinear Fourier multiplier

Sharp Bound for the Generalized m-Linear n-Dimensional Hardy-Littlewood-Polya Operator

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Analysis in Theory and Applications 2023年第1期39卷 28-41页

作者： qianjun he Mingquan Wei Dunyan Yan School of Applied Science Beijing Information Science and Technology UniversityBeijing 100192China School of Mathematics and Statistics Xinyang Normal UniversityXinyang 464000China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper,we calculate the sharp bound for the generalized m-linear n-dimensional Hardy-Littlewood-Polya operator on power weighted central and non-central homogeneous Morrey *** an application,the sharp bound for the Hardy-Littlewood-Polya operator on power weighted central and noncentral homo-geneous Morrey spaces is ***,we also find the sharp bound for the Hausdorff operator on power weighted central and noncentral homogeneous Morrey spaces,which generalizes the previous results.

关键词： Sharp bound n-dimensional Hardy-Littlewood-Polya operator power weight Morrey space Hausdorff operator

Boundedness of the Multilinear Maximal Operator with the Hausdorff Content

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Analysis in Theory and Applications 2023年第1期39卷 42-52页

作者： Shao Liu qianjun he Dunyan Yan School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China School of Applied Science Beijing Information Science and Technology UniversityBeijing 100192China

In this paper,we establish the strong and weak boundedness of the multilinear maximal operator in the setting of the Choquet integral with respect to theαdimensional Hausdorff *** results cover Orobitg and Verdera’s... 详细信息

关键词： Multilinear maximal operator Hausdorff content Choquet integrals

Diffusion Kinetics of Carbonate Hydroxyapatite (CHAP) for Adsorbing F^- Dissolved in Water

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Acta Geologica Sinica(English Edition) 2006年第2期80卷 243-248页

作者： HUANG Zhiliang ZHANG Lianmeng LIU Yu WANG Qilin he qianjun CheN Wei State Key Laboratory of Advanced Technology for Materials Synthesis and Processing Wuhan University of Technology Wuhan Hubei 430070 Research Institute of Mineral Material Wuhan Institute of Technology Wuhan Hubei 430073

A systematic research was performed about diffusion kinetics of adsorbing F^- dissolved in water for carbonate hydroxyapatite （CHAP） from the natural hydroxyapatite which was modified by adulterating with CO3^2-. The result shows that the speed of F^- adsorption is controlled by membrane diffusion when F^- concentration is relatively low, which is expressed by the kinetic equation of diffusion Q=0.0005（Ci-C）（t-ti）＋0.3967, or by vacancy diffusion when F^- concentration is relatively high, which is expressed by the kinetic equation of diffusion In[C（o, t）]=8.4718-0.5048Int. Based on the feature of CHAP for adsorbing F^- dissolved in water and its special channel of the structure of CO3^3- modified hydroxyapatite, models of vacancy diffusion and membrane diffusion were established.

关键词： carbonate hydroxyapatite (CHAP) F^- ion diffusion kinetics

Camptothecin@HMSNs/thermosensitive hydrogel composite for applications in preventing local breast cancer recurrence

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Chinese Chemical Letters 2018年第12期29卷 1819-1823页

作者： Jing Wu Ying Qu Kun Shi Bingyang Chu Yanpeng Jia Xue Xiao qianjun he Zhiyong Qian Department of hematology and Research Laboratory of hematology State Key Laboratory of BiotherapyWest China HospitalSichuan University and Collaborative Innovation Center Department of Gynecology and Obstetrics West China Second University HospitalSichuan University Key Laboratory of Birth Defects and Related Diseases of Women and Children Sichuan UniversityMinistry of Education National-Regional Key Technology Engineering Laboratory for Medical Ultrasound Guangdong Key Laboratory for Biomedical Measurements and Ultrasound ImagingSchool of Biomedical EngineeringShenzhen University

Camptothecin has a strong tumor killing ability for a variety of tumor cells with its special anti-cancer mechanism including the breast cancer. However, because of its infinite hydrophobic property, its clinical application has been greatly limited. Early prevention of loco regional recurrence for the breast cancer is critical for patients who have undergone breast-conserving therapy. In the study,CPT was used for the inhibition of the recurrence after the operation. The hollow mesoporous silica nanoparticles were used as the carrier to improve the hydrophilic property and increase its bioavailability with the high loading capacity. The ability of the cellular uptake and antitumor activity was increased. Hydrogel was the ideal carrier for local therapy, so the CPT@HMSNs were loaded into the PLEL thermo sensitive hydrogel to be injected into the tumor sites after the tumor was resected. The recurrence was reduced in the group of CPT-HMSNs-PLEL and the side effect of CPT was decreased. They exhibit distinguished potential as drug carrier for local delivery.

关键词： Camptothecin Hollow mesoporous silica nanoparticles Breast cancer recurrence Thermosensitive hydrogel Local delivery