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.
In this paper,the parameterized Marcinkiewicz integrals with variable kernels defined by μΩ^ρ（f）（x）=（∫0^∞│∫│1-y│≤t Ω（x,x-y）/│x-y│^n-p f（y）dy│^2dt/t1＋2p）^1/2 are investigated.It is proved that ...In this paper,the parameterized Marcinkiewicz integrals with variable kernels defined by μΩ^ρ（f）（x）=（∫0^∞│∫│1-y│≤t Ω（x,x-y）/│x-y│^n-p f（y）dy│^2dt/t1＋2p）^1/2 are investigated.It is proved that if Ω∈ L∞（R^n） × L^r（S^n-1）（r〉（n-n1p＇/n） is an odd function in the second variable y,then the operator μΩ^ρ is bounded from L^p（R^n） to L^p（R^n） for 1 〈 p ≤ max{（n＋1）/2,2}.It is also proved that,if Ω satisfies the L^1-Dini condition,then μΩ^ρ is of type（p,p） for 1 〈 p ≤ 2,of the weak type（1,1） and bounded from H1 to L1.展开更多
Parameterized computation is a new method dealing with NP-hard problems, which has attracted a lot of attentions in theoretical computer science. As a practical preprocessing method for NP-hard problems, kernelizaiton...Parameterized computation is a new method dealing with NP-hard problems, which has attracted a lot of attentions in theoretical computer science. As a practical preprocessing method for NP-hard problems, kernelizaiton in parameterized computation has recently become an active research area. In this paper, we discuss several kernelizaiton techniques, such as crown decomposition, planar graph vertex partition, randomized methods, and kernel lower bounds, which have been used widely in the kernelization of many hard problems.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.6043302060773111(国家自然科学基金)+1 种基金the Program for New Century Excellent Talents in University of China under Grant No.NCET-05-0683(新世纪优秀人才支持计划)the Program for Changjiang Scholars and Innovative Research Team in University of China under Grant No.IRT0661(长江学者和创新团队发展计划)
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 the National Natural Science Foundation of China (1057115610871173)
文摘In this paper,the parameterized Marcinkiewicz integrals with variable kernels defined by μΩ^ρ（f）（x）=（∫0^∞│∫│1-y│≤t Ω（x,x-y）/│x-y│^n-p f（y）dy│^2dt/t1＋2p）^1/2 are investigated.It is proved that if Ω∈ L∞（R^n） × L^r（S^n-1）（r〉（n-n1p＇/n） is an odd function in the second variable y,then the operator μΩ^ρ is bounded from L^p（R^n） to L^p（R^n） for 1 〈 p ≤ max{（n＋1）/2,2}.It is also proved that,if Ω satisfies the L^1-Dini condition,then μΩ^ρ is of type（p,p） for 1 〈 p ≤ 2,of the weak type（1,1） and bounded from H1 to L1.
基金supported by the National Natural Science Foundation of China (Nos. 61173051, 61103033, and 61232001)
文摘Parameterized computation is a new method dealing with NP-hard problems, which has attracted a lot of attentions in theoretical computer science. As a practical preprocessing method for NP-hard problems, kernelizaiton in parameterized computation has recently become an active research area. In this paper, we discuss several kernelizaiton techniques, such as crown decomposition, planar graph vertex partition, randomized methods, and kernel lower bounds, which have been used widely in the kernelization of many hard problems.
