Endpoint estimates of positive operators in a filtered measure space

2017 ◽  
Vol 109 (5) ◽  
pp. 477-488
Author(s):  
Yahui Zuo ◽  
Lian Wu ◽  
Yong Jiao
Keyword(s):  
Measure Space ◽  
Positive Operators

scholarly journals Positive operators and maximal operators in a filtered measure space

2013 ◽  
Vol 264 (4) ◽  
pp. 920-946 ◽  
Author(s):  
Hitoshi Tanaka ◽  
Yutaka Terasawa
Keyword(s):  
Measure Space ◽  
Positive Operators ◽  
Maximal Operators

An Extrapolation Theorem for Positive Operators

1978 ◽  
Vol 30 (02) ◽  
pp. 225-230
Author(s):  
H. D. B. Miller
Keyword(s):  
Measure Space ◽  
Finite Measure ◽  
Positive Operators ◽  
Vector Spaces ◽  
Complex Vector ◽  
Linear Map ◽  
Positive Linear Map ◽  
Finite Measure Space ◽  
Extrapolation Theorem ◽  
Complex Valued

Denote by S and M respectively the complex vector spaces of simple and measurable complex valued functions defined on the finite measure space X. Let T be a positive linear map from S to M such that for each p, 1 < p < ∞, sup {||T f||p: f ∈ S, ||f||P ≦ 1} is finit. finite. T then has an extension to a bounded transformation of every LP(X), 1 < p < ∞ , and these extensions are "consistent". The norm of T as a transformation of Lp is denoted ||T||P. The aim of this note is to prove the following theorem.

Korovkin Theorems for Integral Operators with Kernels of Finite Oscillation

1974 ◽  
Vol 26 (6) ◽  
pp. 1390-1404 ◽  
Author(s):  
M. J. Marsden ◽  
S. D. Riemenschneider
Keyword(s):  
Banach Space ◽  
Banach Lattice ◽  
Measure Space ◽  
Integral Operators ◽  
Finite Measure ◽  
Bounded Sequence ◽  
Positive Operators ◽  
Linear Operators ◽  
Finite Measure Space

There has been considerable interest recently in the investigation of "Korovkin sets". Briefly, for X a Banach space and a family of linear operators on X, a subset K ⊂ X is a Korovkin set relative to if for any bounded sequence {Tn} ⊂ , Tnk → k in X for each k ∊ K implies Tnx → x for each x ∊ X. A large portion of these investigations have been carried out for X being one of the spaces C(S), S compact Hausdorff, the usual Lp spaces of functions on some finite measure space, or some Banach lattice; while is one of the classes +-positive operators, 1-contractions (i.e., ||T|| 1), or + ⋂1

On the Integrability of the Ergodic Hilbert Transform for A Class of Functions with Equal Absolute Values

1998 ◽  
Vol 5 (2) ◽  
pp. 101-106
Author(s):  
L. Ephremidze
Keyword(s):  
Hilbert Transform ◽  
Measure Space ◽  
Integrable Function ◽  
Finite Measure ◽  
Ergodic Transformation ◽  
Finite Measure Space ◽  
Class Of Functions

Abstract It is proved that for an arbitrary non-atomic finite measure space with a measure-preserving ergodic transformation there exists an integrable function f such that the ergodic Hilbert transform of any function equal in absolute values to f is non-integrable.

Lacunary ideal convergence in measure for sequences of fuzzy valued functions

2021 ◽  
Vol 40 (3) ◽  
pp. 5517-5526
Author(s):  
Ömer Kişi
Keyword(s):  
Measure Space ◽  
Finite Measure ◽  
Ideal Convergence ◽  
Convergence In Measure ◽  
Ideal Form ◽  
Measurable Functions ◽  
Finite Measure Space ◽  
Convergence Of Sequences

We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space ( X , M , μ ) . We also introduce the concept of I θ -convergence in measure for sequences of fuzzy valued functions and proved some significant results.

scholarly journals Fairness and fuzzy coalitions

2021 ◽  
Author(s):  
Chiara Donnini ◽  
Marialaura Pesce
Keyword(s):  
New York ◽  
Economic Theory ◽  
Measure Space ◽  
Exchange Economy ◽  
Mathematical Methods ◽  
Competitive Equilibria ◽  
Fuzzy Coalitions ◽  
Core Allocations

AbstractIn this paper, we study the problem of a fair redistribution of resources among agents in an exchange economy á la Shitovitz (Econometrica 41:467–501, 1973), with agents’ measure space having both atoms and an atomless sector. We proceed by following the idea of Aubin (Mathematical methods of game economic theory. North-Holland, Amsterdam, New York, Oxford, 1979) to allow for partial participation of individuals in coalitions, that induces an enlargement of the set of ordinary coalitions to the so-called fuzzy or generalized coalitions. We propose a notion of fairness which, besides efficiency, imposes absence of envy towards fuzzy coalitions, and which fully characterizes competitive equilibria and Aubin-core allocations.

Convexity Inequalities for Positive Operators

Positivity ◽  
2006 ◽  
Vol 11 (1) ◽  
pp. 57-68 ◽  
Author(s):  
Markus Haase
Keyword(s):  
Positive Operators

scholarly journals Geometry and dynamics of admissible metrics in measure spaces

2013 ◽  
Vol 11 (3) ◽  
Author(s):  
Anatoly Vershik ◽  
Pavel Zatitskiy ◽  
Fedor Petrov
Keyword(s):  
Invariant Measure ◽  
Wide Class ◽  
Lebesgue Space ◽  
Measure Space ◽  
Asymptotic Properties ◽  
Ergodic Transformation ◽  
Measure Spaces ◽  
Admissible Metric ◽  
Discreteness Criterion ◽  
Uniformly Bounded

AbstractWe study a wide class of metrics in a Lebesgue space, namely the class of so-called admissible metrics. We consider the cone of admissible metrics, introduce a special norm in it, prove compactness criteria, define the ɛ-entropy of a measure space with an admissible metric, etc. These notions and related results are applied to the theory of transformations with invariant measure; namely, we study the asymptotic properties of orbits in the cone of admissible metrics with respect to a given transformation or a group of transformations. The main result of this paper is a new discreteness criterion for the spectrum of an ergodic transformation: we prove that the spectrum is discrete if and only if the ɛ-entropy of the averages of some (and hence any) admissible metric over its trajectory is uniformly bounded.

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