Let $G$ be a locally compact group and let $1 \le p < \infty.$ Recently, Chen et al. characterized hypercyclic, supercyclic and chaotic weighted translations on locally compact groups and their homogeneous spaces. There has been an increasing interest in studying the disjoint hypercyclicity acting on various spaces of holomorphic functions. In this note, we will study disjoint hypercyclic and disjoint supercyclic powers of weighted translation operators on the Lebesgue space $L^p(G)$ in terms of the weights. Sufficient and necessary conditions for disjoint hypercyclic and disjoint supercyclic powers of weighted translations generated by aperiodic elements on groups will be given., Liang Zhang, Hui-Qiang Lu, Xiao-Mei Fu, Ze-Hua Zhou., and Obsahuje bibliografické odkazy
The Bruhat order is defined in terms of an interchange operation on the set of permutation matrices of order n which corresponds to the transposition of a pair of elements in a permutation. We introduce an extension of this partial order, which we call the stochastic Bruhat order, for the larger class Ω_{n} of doubly stochastic matrices (convex hull of n×n permutation matrices). An alternative description of this partial order is given. We define a class of special faces of Ω_{n} induced by permutation matrices, which we call Bruhat faces. Several examples of Bruhat faces are given and several results are presented., Richard A. Brualdi, Geir Dahl, Eliseu Fritscher., and Obsahuje seznam literatury
In this paper, characterizations of the embeddings between weighted Copson function spaces ${\rm Cop}_{p_1,q_1}(u_1,v_1)$ and weighted Cesàro function spaces ${\rm Ces}_{p_2,q_2}(u_2,v_2)$ are given. In particular, two-sided estimates of the optimal constant $c$ in the inequality $ \align\biggl( \int_0^{\infty} &\biggl( \int_0^t f(\tau)^{p_2}v_2(\tau)\dd\tau\biggr)^{\!\!\frc{q_2}{p_2}} u_2(t)\dd t\biggr)^{\!\!\frc1{q_2}} $ \ $\le c \biggl( \int_0^{\infty} \biggl( \int_t^{\infty} f(\tau)^{p_1} v_1(\tau)\dd\tau\biggr)^{\!\!\frc{q_1}{p_1}} u_1(t)\dd t\biggr)^{\!\!\frc1{q_1}}, $ where $p_1,p_2,q_1,q_2 \in(0,\infty)$, $p_2 \le q_2$ and $u_1,u_2,v_1,v_2$ are weights on $(0,\infty)$, are obtained. The most innovative part consists of the fact that possibly different parameters $p_1$ and $p_2$ and possibly different inner weights $v_1$ and $v_2$ are allowed. The proof is based on the combination of duality techniques with estimates of optimal constants of the embeddings between weighted Cesàro and Copson spaces and weighted Lebesgue spaces, which reduce the problem to the solutions of iterated Hardy-type inequalities., Amiran Gogatishvili, Rza Mustafayev, Tuğçe Ünver., and Obsahuje bibliografii
Recently, the weak Triebel-Lizorkin space was introduced by Grafakos and He, which includes the standard Triebel-Lizorkin space as a subset. The latter has a wide applications in aspects of analysis. In this paper, the authors firstly give equivalent quasi-norms of weak Triebel-Lizorkin spaces in terms of Peetre's maximal functions. As an application of those equivalent quasi-norms, an atomic decomposition of weak Triebel-Lizorkin spaces is given., Wenchang Li, Jingshi Xu., and Seznam literatury
In this paper, we give some estimates for the essential norm and a new characterization for the boundedness and compactness of weighted composition operators from weighted Bergman spaces and Hardy spaces to the Bloch space., Songxiao Li, Ruishen Qian, Jizhen Zhou., and Obsahuje bibliografické odkazy
We prove L2-maximal regularity of the linear non-autonomous evolutionary Cauchy problem \dot u(t) + A(t)u(t) = f(t){\text{ for a}}{\text{.e}}{\text{. }}t \in \left[ {0,T} \right],{\text{ }}u(0) = {u_0}, where the operator A(t) arises from a time depending sesquilinear form a(t, ·, ·) on a Hilbert space H with constant domain V. We prove the maximal regularity in H when these forms are time Lipschitz continuous. We proceed by approximating the problem using the frozen coefficient method developed by El-Mennaoui, Keyantuo, Laasri (2011), El-Mennaoui, Laasri (2013), and Laasri (2012). As a consequence, we obtain an invariance criterion for convex and closed sets of H., Ahmed Sani, Hafida Laasri., and Obsahuje seznam literatury