齐型空间上的弱Morrey-Herz空间中一类次线性算子交换子的有界性

本文研究了一类次线性算子T和BMO(X)函数b生成的交换子[b,T]的有界性质.利用函数分解方法,获得了[b,T]在WMK˙pα,,qλ(X)上的有界性结果.     

带粗糙核的奇异积分交换子的有界性

本文研究了带粗糙核的奇异积分算子与BMO函数生成的交换子的有界性问题.利用原子分解的方法,获得了带粗糙核的奇异积分交换子TΩb在Lp空间、Hardy空间、弱Hardy空间上的有界性结果,推广了交换子Tb在各类函数空间上有界性的结果.     

Simultaneous state‐time approximation of the chemical master equation using tensor product formats

We apply the novel tensor product formats (tensor train, quantized TT [QTT], and QTT‐Tucker) to the solution of d‐dimensional chemical master equations for gene regulating networks (signaling cascades, toggle switches, and phage‐ λ). For some important cases, for example, signaling cascade models, we prove analytical tensor product representations of the system operator. The quantized tensor representations (QTT, QTT‐Tucker) are employed in both state space and time, and the global state‐time (d + 1)‐dimensional system is solved in the tensor product form by the alternating minimal energy iteration, the ALS‐type algorithm. This approach leads to the logarithmic dependence of the computational complexity on the volume of the state space. We investigate the proposed technique numerically and compare it with the direct chemical master equation solution and some previously known approximate schemes, where possible. We observe that the newer tensor methods demonstrate a good potential in simulation of relevant biological systems. Copyright © 2014 John Wiley & Sons, Ltd.     

A compactness criterion and application to the commutators associated with Schrödinger operators

Let T be an integral operator. In this paper, we introduce a ‐compactness criterion of , where . As an application, we apply this criterion to deal with ‐compactness of commutators associated to Schrödinger operators with potentials in the reverse Hölder's class.     

Lipschitz Estimates for Commutators of p-adic Fractional Hardy Op erators

In this paper, the boundedness of commutators generated by the ndimensional fractional Hardy operators and Lipschitz functions on p-adic function spaces are obtained. The authors show that these commutators are bounded on Herz space and Lebesgue space with suitable indexes. Moreover, the commutator of HardyLittlewood-Poly′a operator is also considered.     

Morrey空间上Marcinkiewicz积分与R

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RBMO（μ）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.     

具有齐性核Marcinkiewicz积分高阶交换子在Herz型Hardy空间中的有界性

讨论了一类具有齐性核的Marcinkiewicz积分高阶交换子在Herz型Hardy空间中的有界性,并得到了其端点估计．     

Singular Hartree equation in fractional perturbed Sobolev spaces

We establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.     

Commutators for Approximation Spaces and Marcinkiewicz-Type Multipliers

It is proved that, under some conditions, weaker than those of the Marcinkiewicz multiplier theorem, the multiplier operator T_μ(∑_k c_ke^ikt)=∑_k μ_kc_ke^ikt satisfies on the Besov space B^σ, q_p the commutator theorem[T, T_μ]_{B^σ, qp, B^σ, qp}c T, where T=max(T_{B^σ0, q0p, B^σ0, q0p}, T_{B^σ1, q1p, B^σ1, q1p} and σ₀>σ>σ₁>0.