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Weak morrey spaces and strong solutions to the Navier-Stokes equations

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Science China Mathematics 2007年第10期50卷 1401-1417页

作者： Chang-xing MIAO~(1+) Bao-quan YUAN~2 ~1 Institute of Applied Physics and Computational Mathematics,P.O.Box 8009,Beijing 100088,China ~2 College of Mathematics and Informatics,Henan Polytechnic University,Jiaozuo 454000,China Institute of Applied Physics and Computational Mathematics Beijing China College of Mathematics and Informatics Henan Polytechnic University Jiaozuo China

We consider the Cauchy problem of Navier-Stokes equations in weak morrey *** first define a class of weak morrey type spaces M_(p,λ)~*(R^n)on the basis of Lorentz space L_(p,∞)=L_p~*(R^n) (in particular,M_(?)~*(R^n)=L_(p,∞),if p>1),and study some fundamental properties of them;Second, we prove that the heat operator U(t)= e^(tΔ)and Calderón-Zygmund singular integral operators are bounded linear operators on weak morrey spaces,and establish the bilinear estimate in weak morrey ***,by means of Kato's method and the contraction mapping principle,we prove that the Cauchy problem of Navier-Stokes equations in weak morrey spaces M_(p,λ)~*(R^n)(1morrey space M_(p,n-p)~*(R^n)can admit the singular initial data with a self-similar *** this paper generalizes Kato's results.

关键词： Navier-Stokes equations, weak morrey spaces, Lorentz spaces, Cauchy problem,time-global well-posedness, self-similar solutions

morrey空间上Marcinkiewicz积分与■交换子

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数学学报（中文版） 2019年第2期62卷 269-278页

作者：陶双平逯光辉西北师范大学数学与统计学院兰州730070

本文建立了Marcinkiewicz积分M与具离散系数的正则有界平均振荡空间■生成的交换子M_b在非齐性度量测度空间上的有界性.在控制函数λ满足∈-弱反双倍条件的假设下,当p∈(1,∞)时,证明了M_b在L^P(μ)上是有界的.另外,还得到了M_b在Morre... 详细信息

本文建立了Marcinkiewicz积分M与具离散系数的正则有界平均振荡空间■生成的交换子M_b在非齐性度量测度空间上的有界性.在控制函数λ满足∈-弱反双倍条件的假设下,当p∈(1,∞)时,证明了M_b在L^P(μ)上是有界的.另外,还得到了M_b在morrey空间上的有界性.

关键词：非齐性度量测度空间 Marcinkiewicz积分交换子 RBMO(μ)空间 morrey 空间

Iterated Commutators for Multilinear Singular Integral Operators on morrey Space with Non-Doubling Measures

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Journal of Applied Mathematics and Physics 2020年第1期8卷 53-69页

作者： Tie Li Yinsheng Jiang Yaoming Niu Baotou Teacher’s College of Inner Mongolia University of Science and Technology Baotou China

Let μ be a non-negative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that μ(B(x,r)) ≤ Crn?for all x∈ Rd, r > 0 and some fixed n ∈ (0,d]. This paper is interested in the properties of the iterated commutators of multilinear singular integral operators on morrey spaces?.Precisely speaking, we show that the iterated commutators generated by multilinear singular integrals operators are bounded from to where (Regular Bounded Mean Oscillation space) and 1 qj ≤ pj ∞ with 1/p = 1/p1 + ... + 1/pm and 1/q = 1/q1+ ... + 1/qm.

关键词： Non-Doubling Measures morrey Space Multilinear Singular Integral Operators RBMO Commutator

Herz空间与Herz型morrey空间上的算子

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Herz空间与Herz型Morrey空间上的算子

作者：赵向青新疆大学

学位级别：硕士

LpSρ^m拟微分算子在morrey空间上的估计

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湘潭大学学报（自然科学版） 2020年第2期42卷 83-88页

作者：周游邓宇龙龙顺潮湘潭大学数学与计算科学学院湖南湘潭411105

该文给出了LpSρ^m拟微分算子在morrey空间上的有界性.令1

关键词： Hardy-Littlewood 极大算子拟微分算子 morrey 空间

Generalized Schwarzian Derivatives and Analytic morrey Spaces

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Chinese Quarterly Journal of Mathematics 2019年第2期34卷 171-187页

作者： JIN Jian-jun LI Hua-bing TANG Shu-an School of Mathematics Sciences Hefei University of TechnologyXuancheng CampusXuancheng242000China School of Mathematics Sciences Guizhou Normal UniversityGuiyang550001China

In this paper,we study univalent functions f for which log f’belongs to the analytic morrey *** using the characterization of higher order derivatives of functions in analytic morrey spaces,we establish some new desc... 详细信息

关键词： Analytic morrey spaces univalent functions Schwarzian derivative generalized Schwarzian derivatives Carleson measure

Distal biceps tendon rupture reconstruction using musclesplitting double-incision approach

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World Journal of Clinical Cases 2014年第8期2卷 357-361页

作者： Luigi Tarallo Raffaele Mugnai Francesco Zambianchi Roberto Adani Fabio Catani Orthopaedics and Traumatology Department Modena PoliclinicUniversity of Modena and Reggio Emilia41124 ModenaItaly Department of Hand Surgery and Microsurgery University Hospital of Verona37134 VeronaItaly

AIM: To evaluate the clinical and functional results after repair of distal biceps tendon tears, following the morrey's modified double-incision ***: We retrospectively reviewed 47 patients with distal rupture of biceps brachii treated between2003 and 2012 in our Orthopedic Department with muscle-splitting double-incision technique. Outcome measures included the Mayo elbow performance, the DASH questionnaire, patient's satisfaction, elbow and forearm motion, grip strength and complications ***: At an average 18 mo follow-up(range, 7 mo-10 years) the average Mayo elbow performance and DASH score were respectively 97.2 and 4.8. The elbow flexion range was 94%, extension was-2°, supination was 93% and pronation 96% compared with the uninjured limb. The mean grip strength, expressed as percentage of respective contralateral limb, was 83%. The average patient satisfaction rating on a Likert scale(from 0 to 10) was 9.4. The following complications were observed: 3 cases of heterotopic ossification(6.4%), one(2.1%) re-rupture of the tendon at the site of reattachment and 2 cases(4.3%) of posterior interosseous nerve palsy. No complication required further surgical ***: This technique allows an anatomic reattachment of distal biceps tendon at the radial tuberosity providing full functional recovery with low complication rate.

关键词： Distal biceps tendon Rupture Double incision Complications Clinical outcome Trans-osseous tunnels morrey