scholarly journals Multiplication Operators between Lipschitz-Type Spaces on a Tree

2011 ◽  
Vol 2011 ◽  
pp. 1-36 ◽  
Author(s):  
Robert F. Allen ◽  
Flavia Colonna ◽  
Glenn R. Easley
Keyword(s):  
Essential Norm ◽  
Operator Norm ◽  
Multiplication Operators ◽  
Norm Estimates ◽  
Infinite Tree ◽  
Type Spaces ◽  
Bounded Functions ◽  
The Difference ◽  
Complex Valued

Let be the space of complex-valued functions on the set of vertices of an infinite tree rooted at such that the difference of the values of at neighboring vertices remains bounded throughout the tree, and let be the set of functions such that , where is the distance between and and is the neighbor of closest to . In this paper, we characterize the bounded and the compact multiplication operators between and and provide operator norm and essential norm estimates. Furthermore, we characterize the bounded and compact multiplication operators between and the space of bounded functions on and determine their operator norm and their essential norm. We establish that there are no isometries among the multiplication operators between these spaces.

Essential norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2877-2889 ◽  
Author(s):  
Amir Sanatpour ◽  
Mostafa Hassanlou
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Essential Norm ◽  
Necessary And Sufficient Conditions ◽  
Norm Estimates ◽  
Type Spaces ◽  
Necessary And Sufficient

We study boundedness of weighted differentiation composition operators Dk?,u between Zygmund type spaces Z? and Bloch type spaces ?. We also give essential norm estimates of such operators in different cases of k ? N and 0 < ?,? < ?. Applying our essential norm estimates, we get necessary and sufficient conditions for the compactness of these operators.

scholarly journals Inequalities Involving Essential Norm Estimates of Product-Type Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Manisha Devi ◽  
Ajay K. Sharma ◽  
Kuldip Raj
Keyword(s):  
Analytic Function ◽  
Holomorphic Function ◽  
Weighted Composition Operator ◽  
Essential Norm ◽  
Open Unit ◽  
Open Unit Disk ◽  
Norm Estimates ◽  
Type Spaces ◽  
Weighted Composition ◽  
Dirichlet Type Spaces

Consider an open unit disk D = z ∈ ℂ : z < 1 in the complex plane ℂ , ξ a holomorphic function on D , and ψ a holomorphic self-map of D . For an analytic function f , the weighted composition operator is denoted and defined as follows: W ξ , ψ f z = ξ z f ψ z . We estimate the essential norm of this operator from Dirichlet-type spaces to Bers-type spaces and Bloch-type spaces.

Essential norm estimates for multiplication operators on $$L_p(\mu )$$ spaces

2021 ◽  
Author(s):  
René E. Castillo ◽  
Yesid A. Lemus-Abril ◽  
Julio C. Ramos-Fernández
Keyword(s):  
Essential Norm ◽  
Multiplication Operators ◽  
Norm Estimates

scholarly journals Optimal minimax rates against non-smooth alternatives

2021 ◽  
Author(s):  
Kohtaro Hitomi ◽  
Masamune Iwasawa ◽  
Yoshihiko Nishiyama
Keyword(s):  
Alternative Hypothesis ◽  
Error Variance ◽  
Smooth Functions ◽  
Engel Curves ◽  
Minimax Rates ◽  
Instrumental Variable Regression ◽  
Bounded Functions ◽  
The Difference ◽  
Set Up ◽  
Minimax Rate

Abstract This study investigates optimal minimax rates for specification testing when the alternative hypothesis is built on a set of non-smooth functions. The set consists of bounded functions that are not necessarily differentiable with no smoothness constraints imposed on their derivatives. In the instrumental variable regression set up with an unknown error variance structure, we find that the optimal minimax rate is n−1/4, where n is the sample size. The rate is achieved by a simple test based on the difference between non-parametric and parametric variance estimators. Simulation studies illustrate that the test has reasonable power against various non-smooth alternatives. The empirical application to Engel curves specification emphasizes the good applicability of the test.

scholarly journals On Complex-Valued Triple Controlled Metric Spaces and Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Nabil Mlaiki ◽  
Thabet Abdeljawad ◽  
Wasfi Shatanawi ◽  
Hassen Aydi ◽  
Yaé Ulrich Gaba
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Polynomial Equations ◽  
Degree Polynomial ◽  
Fredholm Type ◽  
Type Integral ◽  
Type Spaces ◽  
Complex Valued

In this manuscript, we introduce the concept of complex-valued triple controlled metric spaces as an extension of rectangular metric type spaces. To validate our hypotheses and to show the usability of the Banach and Kannan fixed point results discussed herein, we present an application on Fredholm-type integral equations and an application on higher degree polynomial equations.

A Best Possible Tauberian Theorem for the Collective Continuous Hausdorff Summability Method

1971 ◽  
Vol 23 (3) ◽  
pp. 544-549
Author(s):  
G. E. Peterson
Keyword(s):  
Hausdorff Spaces ◽  
Locally Compact ◽  
Compact Spaces ◽  
Bounded Complex ◽  
Hausdorff Method ◽  
Borel Functions ◽  
Bounded Functions ◽  
Abelian Theorem ◽  
Complex Valued ◽  
Locally Compact Spaces

The purpose of this paper is to prove that o(l/x) is the best possible Tauberian condition for the collective continuous Hausdorff method of summation. The analogue of this result for the collective (discrete) Hausdorff method is known [1, pp. 229, ff.; 7, p. 318; 8, p. 254]. Our method involves generalizing a well-known Abelian theorem of Agnew [2] to locally compact spaces and then applying the analogue for integrals of a result Lorentz obtained for series [6, Theorem 1].Let T and X denote locally compact, non compact, σ-compact Hausdorff spaces. Let T′ = T ∪ (∞) and X′ = X ∪ (∞) denote the onepoint compactifications of T and X, respectively. Let B(T) denote the set of locally bounded, complex valued Borel functions on T and let B∞(T) denote the bounded functions in B(T).

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