This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtai...This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesaro oper- ators （with symbols in central BMO spaces） are bounded on the product of central Morrey spaces. These results extends known results on multilinear Hardy operators.展开更多
Probabilistic linear （N, δ）-widths and p-average linear N-widths of Sobolev space W2^r（T）, equipped with a Gaussian probability measure #, are studied in the metric of Sq （T） （1 ≤ Q ≤∞）, and determined the...Probabilistic linear （N, δ）-widths and p-average linear N-widths of Sobolev space W2^r（T）, equipped with a Gaussian probability measure #, are studied in the metric of Sq （T） （1 ≤ Q ≤∞）, and determined the asymptotic equalities：λN,δ（W2^r（T）,μ,Sq（T））={（N^-1）^r＋p/2-1/q√1＋1/N·ln1/δ, 1≤q≤2, （N^-1）^r＋p/2-1/q（1＋N^-1/q√ln1/δ）,2〈q〈∞, （N^-1）^r＋p/2√lnN/δ, q=∞,and λN^（a）（W2^r（T）,μ,Sq（T））p={（N^-1）^r＋p/2-1/q, 1≤q〈∞, （N^-1）^r＋p/2-1/q√lnN, q=∞,where 0 〈 p 〈 ∞, δ∈ （0, 1/2], ρ 〉 1, and Sq（T） is a subspace of L1（T）, in which the Fourier series is absolutely convergent in lq sense.展开更多
We study the average position and the symmetry of the distribution in the SU（2） open quantum random walk （OQRW）. We show that the average position in the central limit theorem （CLT） is non-uniform compared with ...We study the average position and the symmetry of the distribution in the SU（2） open quantum random walk （OQRW）. We show that the average position in the central limit theorem （CLT） is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT.展开更多
基金supported by Vietnam National Foundation for Science and Technology Development(101.02-2014.51)
文摘This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesaro oper- ators （with symbols in central BMO spaces） are bounded on the product of central Morrey spaces. These results extends known results on multilinear Hardy operators.
基金partially supported by National Nature Science Foundation of China(61372187)Sichuan Key Technology Research and Development Program(2012GZ0019,2013GXZ0155)the Fund of Lab of Security Insurance of Cyberspace,Sichuan Province(szjj2014-079)
文摘Probabilistic linear （N, δ）-widths and p-average linear N-widths of Sobolev space W2^r（T）, equipped with a Gaussian probability measure #, are studied in the metric of Sq （T） （1 ≤ Q ≤∞）, and determined the asymptotic equalities：λN,δ（W2^r（T）,μ,Sq（T））={（N^-1）^r＋p/2-1/q√1＋1/N·ln1/δ, 1≤q≤2, （N^-1）^r＋p/2-1/q（1＋N^-1/q√ln1/δ）,2〈q〈∞, （N^-1）^r＋p/2√lnN/δ, q=∞,and λN^（a）（W2^r（T）,μ,Sq（T））p={（N^-1）^r＋p/2-1/q, 1≤q〈∞, （N^-1）^r＋p/2-1/q√lnN, q=∞,where 0 〈 p 〈 ∞, δ∈ （0, 1/2], ρ 〉 1, and Sq（T） is a subspace of L1（T）, in which the Fourier series is absolutely convergent in lq sense.
文摘We study the average position and the symmetry of the distribution in the SU（2） open quantum random walk （OQRW）. We show that the average position in the central limit theorem （CLT） is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT.
