Zobrazeno 1 - 10
of 153
pro vyhledávání: '"Hong, Guixiang"'
Autor:
Chen, Cheng, Hong, Guixiang
In this paper, we establish a noncommutative spherical maximal inequality associated with automorphisms on von Neumann algebras, extending Magyar-Stein-Wainger's discrete spherical maximal inequality to the noncommutative setting.
Comment: 16 pa
Comment: 16 pa
Externí odkaz:
http://arxiv.org/abs/2410.06035
Autor:
Hong, Guixiang, Jing, Yuanyuan
We study the Campanato spaces associated with quantum Markov semigroups on a finite von Neumann algebra $\mathcal M$. Let $\mathcal T=(T_{t})_{t\geq0}$ be a Markov semigroup, $\mathcal P=(P_{t})_{t\geq0}$ the subordinated Poisson semigroup and $\alph
Externí odkaz:
http://arxiv.org/abs/2409.14414
In this paper, we establish a noncommutative maximal inequality for ergodic averages with respect to the set $\{k^t|k=1,2,3,...\}$ acting on noncommutative $L_p$ spaces for $p>\frac{\sqrt{5}+1}{2}$.
Comment: 18 pages
Comment: 18 pages
Externí odkaz:
http://arxiv.org/abs/2408.04374
In this paper, we explore Fourier analysis for noncommutative $L_p$ space-valued functions on $G$, where $G$ is a totally disconnected non-abelian compact group. By additionally assuming that the value of these functions remains invariant within each
Externí odkaz:
http://arxiv.org/abs/2403.09263
Autor:
Hong, Guixiang, Ricard, Éric
In this paper, we provide a counterexample to show that in sharp contrast to the classical case, the almost uniform convergence may not happen for truly noncommutative $L_p$-martingales when $1\leq p<2$. The same happens to ergodic averages. The proo
Externí odkaz:
http://arxiv.org/abs/2402.08560
Let $L$ be a sectorial operator of type $\alpha$ ($0 \leq \alpha < \pi/2$) on $L^2(\mathbb{R}^d)$ with the kernels of $\{e^{-tL}\}_{t>0}$ satisfying certain size and regularity conditions. Define $$ S_{q,L}(f)(x) = \left(\int_0^{\infty}\int_{|y-x| <
Externí odkaz:
http://arxiv.org/abs/2401.13932
In this paper, the authors study the matrix-valued harmonic functions and characterize them by the Poisson integral of functions in non-commutative BMO (bounded mean oscillation) spaces. This provides a very satisfactory non-commutative analogue of t
Externí odkaz:
http://arxiv.org/abs/2309.11752
In this article, we establish sharp endpoint $L_p$ estimates of Schr\"odinger groups on general measure spaces which may not be equipped with good metrics but admit submarkovian semigroups satisfying purely algebraic assumptions. One of the key ingre
Externí odkaz:
http://arxiv.org/abs/2302.00435
In this paper, we establish the quantitative mean ergodic theorems for two subclasses of power bounded operators on a fixed noncommutative $L_p$-space with $1
Externí odkaz:
http://arxiv.org/abs/2301.00186
In this paper, we obtain the desired noncommutative maximal inequalities of the truncated Calder\'on-Zygmund operators of non-convolution type acting on operator-valued $L_p$-functions for all $1
Externí odkaz:
http://arxiv.org/abs/2212.13150