本文研究了一类带外力项的广义半线性抛物方程在抛物型Morrey空间Mαp1,k(d+α)α−β中的整体适定性问题。该方程包含分数阶拉普拉斯算子耗散项、非局部非线性项及一般外力项,其形式为ut+(−Δ)α2u=(−Δ)β2(| u |ku)+f,其中βα(k+1)β...本文研究了一类带外力项的广义半线性抛物方程在抛物型Morrey空间Mαp1,k(d+α)α−β中的整体适定性问题。该方程包含分数阶拉普拉斯算子耗散项、非局部非线性项及一般外力项,其形式为ut+(−Δ)α2u=(−Δ)β2(| u |ku)+f,其中βα(k+1)β(亚临界情形)。该模型具有高度的普适性,通过参数选取可退化为多个经典物理模型。本文通过Duhamel原理将初值问题转化为等价的积分方程,在线性项、非线性项及外力项满足充分小范数的条件下,系统建立了各项在所选空间中的关键先验估计。最终,应用Banach不动点定理,证明了该方程整体温和解在抛物型Morrey空间中的存在性、唯一性及对初值的连续依赖性。本研究推广了现有经典结果,彰显了抛物型Morrey空间为处理此类兼具非局部结构与临界增长的非线性发展方程提供了统一而有效的分析工具。展开更多
In this paper,the authors study the fractional Calderon type commutator T_(Ω,α)^(A)and its maximal operator M_(Ω,α)^(A)with kernels having some kinds of Log-type Dini-condition and obtain the compactness on Morrey...In this paper,the authors study the fractional Calderon type commutator T_(Ω,α)^(A)and its maximal operator M_(Ω,α)^(A)with kernels having some kinds of Log-type Dini-condition and obtain the compactness on Morrey spaces L^(p,λ)(R^(n)).展开更多
利用Hardy-Littlewood极大算子的加权有界性和Sharp极大函数的点态估计等工具,给出RD(reverse doubling)-空间上多线性强奇异Calderón-Zygmund算子及其与BMO(bounded mean oscillation)函数生成的多线性交换子在加权乘积Morrey空...利用Hardy-Littlewood极大算子的加权有界性和Sharp极大函数的点态估计等工具,给出RD(reverse doubling)-空间上多线性强奇异Calderón-Zygmund算子及其与BMO(bounded mean oscillation)函数生成的多线性交换子在加权乘积Morrey空间上的有界性.展开更多
This paper considers compactness of the commutator[b,I_(α)]i(i=1,2),where I_(α)is a bilinear fractional integral operator,and b is a function in generalized Campanato spaces with variable growth condition.The author...This paper considers compactness of the commutator[b,I_(α)]i(i=1,2),where I_(α)is a bilinear fractional integral operator,and b is a function in generalized Campanato spaces with variable growth condition.The author gives sufficient conditions for the compactness of[b,I_(α)],(i=1,2)from the product of generalized Morrey spaces to generalized Morrey spaces.展开更多
In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding res...In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding results of multilinear Galderón-gygmund operator can be obtained.展开更多
文摘本文研究了一类带外力项的广义半线性抛物方程在抛物型Morrey空间Mαp1,k(d+α)α−β中的整体适定性问题。该方程包含分数阶拉普拉斯算子耗散项、非局部非线性项及一般外力项,其形式为ut+(−Δ)α2u=(−Δ)β2(| u |ku)+f,其中βα(k+1)β(亚临界情形)。该模型具有高度的普适性,通过参数选取可退化为多个经典物理模型。本文通过Duhamel原理将初值问题转化为等价的积分方程,在线性项、非线性项及外力项满足充分小范数的条件下,系统建立了各项在所选空间中的关键先验估计。最终,应用Banach不动点定理,证明了该方程整体温和解在抛物型Morrey空间中的存在性、唯一性及对初值的连续依赖性。本研究推广了现有经典结果,彰显了抛物型Morrey空间为处理此类兼具非局部结构与临界增长的非线性发展方程提供了统一而有效的分析工具。
文摘In this paper,the authors study the fractional Calderon type commutator T_(Ω,α)^(A)and its maximal operator M_(Ω,α)^(A)with kernels having some kinds of Log-type Dini-condition and obtain the compactness on Morrey spaces L^(p,λ)(R^(n)).
文摘利用Hardy-Littlewood极大算子的加权有界性和Sharp极大函数的点态估计等工具,给出RD(reverse doubling)-空间上多线性强奇异Calderón-Zygmund算子及其与BMO(bounded mean oscillation)函数生成的多线性交换子在加权乘积Morrey空间上的有界性.
基金Supported by the Key Project of the Education Department of Fujian Province(JZ230054)the Sanming University's High-Level Talent Introduction Project(23YG09)the Natural Science Foundation of Fujian Province(2024J01903)。
文摘This paper considers compactness of the commutator[b,I_(α)]i(i=1,2),where I_(α)is a bilinear fractional integral operator,and b is a function in generalized Campanato spaces with variable growth condition.The author gives sufficient conditions for the compactness of[b,I_(α)],(i=1,2)from the product of generalized Morrey spaces to generalized Morrey spaces.
基金Supported by the the National Natural Science Foundation of China (10571014) the Doctoral Programme Foundation of Institution of Higher Education of China (20040027001).
文摘In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding results of multilinear Galderón-gygmund operator can be obtained.
基金partially supported by NSFC(No.11271175,No.11301249)NSF of Shandong Province(No.ZR2012AQ026)Applied Mathematics Enhancement Program of Linyi University
