In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale in...In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale inequalities of mixed quasi-martingale Hardy spaces.Moreover,we furnish sufficient conditions for the boundedness ofσ-sublinear operators in these spaces.These findings extend the existing conclusions regarding mixed quasi-martingale Hardy spaces defined with the help of the mixed L_(p)-norm.展开更多
The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) i...The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) into Lq(Rn) when 0<p≤1 and 1/q=1/p-α/n.The results in this paper improve the results obtained by Ding,Chen and Fan in 2002.展开更多
Let α≥ 0 and 0 〈 ρ ≤ n/2, the boundedness of hypersingular parameterized Marcinkiewicz integrals μΩ,α^ρ with variable kernels on Sobolev spaces Lα^ρ and HardySobolev spaces Hα^ρ is established.
This article obtains an explicit expression of the heat kernels on H-type groups and then follow the estimate of heat kernels to deduce the Hardy＇s uncertainty principle on the nilpotent Lie groups.
The authors discuss Lipschitz boundedness for a class of fractional multilinear operators with variable kernels. It is obtained that these operators are both Lipschitz bounded from L^p to H^q.
By the characterization of the matrix Hilbert transform in the Hermitian Clifford analysis, we introduce the matrix Szeg5 projection operator for the Hardy space of Hermitean monogenic functions defined on a bounded s...By the characterization of the matrix Hilbert transform in the Hermitian Clifford analysis, we introduce the matrix Szeg5 projection operator for the Hardy space of Hermitean monogenic functions defined on a bounded sub-domain of even dimensional Euclidean space, establish the Kerzman-Stein formula which closely connects the matrix Szego projection operator with the Hardy projection operator onto the Hardy space, and get the matrix Szego projection operator in terms of the Hardy projection operator and its adjoint. Furthermore, we construct the explicit matrix Szego kernel function for the Hardy space on the sphere as an example, and get the solution to a boundary value problem for matrix functions.展开更多
In this paper, the authors study the multilinear operators with Dini Kernel and obtain their boundedness from Herz spaces to Herz-type Hardy spaces. Moreover, the authors also consider the corresponding fractional ope...In this paper, the authors study the multilinear operators with Dini Kernel and obtain their boundedness from Herz spaces to Herz-type Hardy spaces. Moreover, the authors also consider the corresponding fractional operators.展开更多
The more explicit decomposition of the operator and the kernel are utilized to investigate a characterization of the central BMO(R^(n))-closure of C^(∞)(R^(n))space via the compactness of the commutators of fractiona...The more explicit decomposition of the operator and the kernel are utilized to investigate a characterization of the central BMO(R^(n))-closure of C^(∞)(R^(n))space via the compactness of the commutators of fractional Hardy operator with rough kernel.展开更多
In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequen...In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequence of L^(1)functions converging to the given function and verifying their representation in the form of Fourier transform to establish the desired result of the given function.Applying this main result,we further generalize the Paley-Wiener theorem for band-limited functions to the analytic function spaces L^(p)(0<p<∞)with general weights.展开更多
基金Supported by the National Natural Science Foundation of China(11871195)。
文摘In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale inequalities of mixed quasi-martingale Hardy spaces.Moreover,we furnish sufficient conditions for the boundedness ofσ-sublinear operators in these spaces.These findings extend the existing conclusions regarding mixed quasi-martingale Hardy spaces defined with the help of the mixed L_(p)-norm.
基金Supported by the973Project( G1 9990 75 1 0 5 ) and the National Natural Science Foundation of China( 1 0 2 71 0 1 6)
文摘The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) into Lq(Rn) when 0<p≤1 and 1/q=1/p-α/n.The results in this paper improve the results obtained by Ding,Chen and Fan in 2002.
基金Supported by the National Natural Science Foundation of China(1057115610871173)
文摘Let α≥ 0 and 0 〈 ρ ≤ n/2, the boundedness of hypersingular parameterized Marcinkiewicz integrals μΩ,α^ρ with variable kernels on Sobolev spaces Lα^ρ and HardySobolev spaces Hα^ρ is established.
基金supported by National Science Foundation of China (10571044)
文摘This article obtains an explicit expression of the heat kernels on H-type groups and then follow the estimate of heat kernels to deduce the Hardy＇s uncertainty principle on the nilpotent Lie groups.
基金Supported by Zhejiang Provincial Natural Science Foundation of China under Grant (No.M103069)supported by the Education Dept. of Zhejiang Province(20021022)
文摘The authors discuss Lipschitz boundedness for a class of fractional multilinear operators with variable kernels. It is obtained that these operators are both Lipschitz bounded from L^p to H^q.
基金supported by Portuguese funds through the CIDMA Center for Research and Development in Mathematics and Applicationsthe Portuguese Foundation for Science and Technology(FCT–Fundao para a Ciência e a Tecnologia)within project UID/MAT/04106/2013the recipient of a Postdoctoral Foundation from FCT under Grant No. SFRH/BPD/74581/2010
文摘By the characterization of the matrix Hilbert transform in the Hermitian Clifford analysis, we introduce the matrix Szeg5 projection operator for the Hardy space of Hermitean monogenic functions defined on a bounded sub-domain of even dimensional Euclidean space, establish the Kerzman-Stein formula which closely connects the matrix Szego projection operator with the Hardy projection operator onto the Hardy space, and get the matrix Szego projection operator in terms of the Hardy projection operator and its adjoint. Furthermore, we construct the explicit matrix Szego kernel function for the Hardy space on the sphere as an example, and get the solution to a boundary value problem for matrix functions.
文摘In this paper, the authors study the multilinear operators with Dini Kernel and obtain their boundedness from Herz spaces to Herz-type Hardy spaces. Moreover, the authors also consider the corresponding fractional operators.
基金supported by National Natural Science Foundation of China (11001002, 10926061)the Beijing Foundation Program (201010009009, 2010D005002000002)+1 种基金supported by National Natural Science Foundation of China (10871003, 10990012)the Specialized Research Fund for the Doctoral Program of Higher Education of China (2007001040)
文摘In this article, we prove a heat kernel version of Hardy＇s theorem for the Laguerre hypergroup.
基金supported by the NSF of China(Grant Nos.11771195,and 12071197)the NSF of Shandong Province(Grant Nos.ZR2019YQ04,2020KJI002,and 2019KJI003)the key Laboratory of Complex Systems and Intelligent Computing in University of Shandong(Linyi University).
文摘The more explicit decomposition of the operator and the kernel are utilized to investigate a characterization of the central BMO(R^(n))-closure of C^(∞)(R^(n))space via the compactness of the commutators of fractional Hardy operator with rough kernel.
基金Supported by the National Natural Science Foundation of China(12301101)the Guangdong Basic and Applied Basic Research Foundation(2022A1515110019 and 2020A1515110585)。
文摘In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequence of L^(1)functions converging to the given function and verifying their representation in the form of Fourier transform to establish the desired result of the given function.Applying this main result,we further generalize the Paley-Wiener theorem for band-limited functions to the analytic function spaces L^(p)(0<p<∞)with general weights.
