Pettis mean convergence of vector-valued asymptotic martingales

1977 ◽  
Vol 37 (4) ◽  
pp. 291-295 ◽  
Author(s):  
J. J. Uhl
Keyword(s):  
Mean Convergence ◽  
Vector Valued

scholarly journals Mean Convergence of Vector-valued Walsh Series

1993 ◽  
Vol 162 (1) ◽  
pp. 117-124 ◽  
Author(s):  
Jörg Wenzel
Keyword(s):  
Walsh Series ◽  
Mean Convergence ◽  
Vector Valued

scholarly journals UNIFORM INTEGRABILITY AND MEAN CONVERGENCE FOR THE VECTOR-VALUED MCSHANE INTEGRAL

1997 ◽  
Vol 23 (1) ◽  
pp. 303 ◽  
Author(s):  
Swartz
Keyword(s):  
Uniform Integrability ◽  
Mean Convergence ◽  
Mcshane Integral ◽  
Vector Valued

The Vector-Valued Maximin

1994 ◽  
Keyword(s):  
Vector Valued

Trade-Off and Consensus in Vector-Valued Optimization Theory

2001 ◽  
Vol 33 (9) ◽  
pp. 10
Author(s):  
Albert N. Voronin
Keyword(s):  
Optimization Theory ◽  
Trade Off ◽  
Vector Valued

The range of block Hankel operators

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3237-3243
Author(s):  
In Hwang ◽  
In Kim ◽  
Sumin Kim
Keyword(s):  
Hardy Space ◽  
Invariant Subspace ◽  
Hankel Operators ◽  
Coprime Factorization ◽  
Backward Shift ◽  
Vector Valued

In this note we give a connection between the closure of the range of block Hankel operators acting on the vector-valued Hardy space H2Cn and the left coprime factorization of its symbol. Given a subset F ? H2Cn, we also consider the smallest invariant subspace S*F of the backward shift S* that contains F.

Operators from H1 into a Banach space and vector valued measures

1989 ◽  
pp. 87-93
Author(s):  
Oscar Blasco
Keyword(s):  
Banach Space ◽  
Vector Valued

Generic rotation sets

2020 ◽  
pp. 1-13
Author(s):  
SEBASTIÁN PAVEZ-MOLINA
Keyword(s):  
Dynamical System ◽  
Convex Body ◽  
Probability Measures ◽  
Topological Dynamical System ◽  
Continuous Vector ◽  
Rotation Set ◽  
Vector Valued Function ◽  
Vector Valued ◽  
Uniquely Ergodic ◽  
Dense Set

Abstract Let $(X,T)$ be a topological dynamical system. Given a continuous vector-valued function $F \in C(X, \mathbb {R}^{d})$ called a potential, we define its rotation set $R(F)$ as the set of integrals of F with respect to all T-invariant probability measures, which is a convex body of $\mathbb {R}^{d}$ . In this paper we study the geometry of rotation sets. We prove that if T is a non-uniquely ergodic topological dynamical system with a dense set of periodic measures, then the map $R(\cdot )$ is open with respect to the uniform topologies. As a consequence, we obtain that the rotation set of a generic potential is strictly convex and has $C^{1}$ boundary. Furthermore, we prove that the map $R(\cdot )$ is surjective, extending a result of Kucherenko and Wolf.

A weak vector-valued Banach–Stone theorem for Choquet simplices

2021 ◽  
Author(s):  
Jakub Rondoš ◽  
Jiří Spurný
Keyword(s):  
Vector Valued ◽  
Stone Theorem ◽  
Weak Vector

scholarly journals A note on singular integrals with angular integrability

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Feng Liu
Keyword(s):  
Singular Integral ◽  
Singular Integrals ◽  
Function Spaces ◽  
Riesz Transforms ◽  
Hilbert Transforms ◽  
Rotation Method ◽  
Vector Valued Function ◽  
Vector Valued ◽  
L Log L

Abstract In this note we study the rough singular integral $$ T_{\varOmega }f(x)=\mathrm{p.v.} \int _{\mathbb{R}^{n}}f(x-y)\frac{\varOmega (y/ \vert y \vert )}{ \vert y \vert ^{n}}\,dy, $$ T Ω f ( x ) = p . v . ∫ R n f ( x − y ) Ω ( y / | y | ) | y | n d y , where $n\geq 2$ n ≥ 2 and Ω is a function in $L\log L(\mathrm{S} ^{n-1})$ L log L ( S n − 1 ) with vanishing integral. We prove that $T_{\varOmega }$ T Ω is bounded on the mixed radial-angular spaces $L_{|x|}^{p}L_{\theta }^{\tilde{p}}( \mathbb{R}^{n})$ L | x | p L θ p ˜ ( R n ) , on the vector-valued mixed radial-angular spaces $L_{|x|}^{p}L_{\theta }^{\tilde{p}}(\mathbb{R}^{n},\ell ^{\tilde{p}})$ L | x | p L θ p ˜ ( R n , ℓ p ˜ ) and on the vector-valued function spaces $L^{p}(\mathbb{R}^{n}, \ell ^{\tilde{p}})$ L p ( R n , ℓ p ˜ ) if $1<\tilde{p}\leq p<\tilde{p}n/(n-1)$ 1 < p ˜ ≤ p < p ˜ n / ( n − 1 ) or $\tilde{p}n/(\tilde{p}+n-1)< p\leq \tilde{p}<\infty $ p ˜ n / ( p ˜ + n − 1 ) < p ≤ p ˜ < ∞ . The same conclusions hold for the well-known Riesz transforms and directional Hilbert transforms. It should be pointed out that our proof is based on the Calderón–Zygmund’s rotation method.

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