scholarly journals Boundedness of Commutators of a Class of Generalized Calderón-Zygmund Operators on Lebesgue Space with Variable Exponent

2012 ◽  
Vol 02 (02) ◽  
pp. 78-81 ◽  
Author(s):  
丽娜 马
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent

Approximation by trigonometric polynomials in the framework of variable exponent grand Lebesgue spaces

2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Nina Danelia ◽  
Vakhtang Kokilashvili
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Trigonometric Polynomials ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Space ◽  
Grand Lebesgue Spaces ◽  
Direct And Inverse Theorems ◽  
Inverse Theorems ◽  
Grand Lebesgue Space

AbstractIn this paper we establish direct and inverse theorems on approximation by trigonometric polynomials for the functions of the closure of the variable exponent Lebesgue space in the variable exponent grand Lebesgue space.

scholarly journals A Necessary and Sufficient Condition for Hardy’s Operator in the Variable Lebesgue Space

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Farman Mamedov ◽  
Yusuf Zeren
Keyword(s):  
Hardy Inequality ◽  
Lebesgue Space ◽  
Variable Exponent ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Variable Lebesgue Space ◽  
Necessary And Sufficient

The variable exponent Hardy inequalityxβ(x)-1∫0x‍f(t)dtLp(.)(0,l)≤Cxβ(x)fLp(.)(0,l),f≥0is proved assuming that the exponentsp:(0,l)→(1,∞),β:(0,l)→ℝnot rapidly oscilate near origin and1/p′(0)-β>0. The main result is a necessary and sufficient condition onp,βgeneralizing known results on this inequality.

scholarly journals Weak Type Estimates of Variable Kernel Fractional Integral and Their Commutators on Variable Exponent Morrey Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Xukui Shao ◽  
Shuangping Tao
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Variable Kernel ◽  
Fractional Integral Operators ◽  
Weak Type Estimates ◽  
Weak Morrey Spaces

In this paper, the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent weak Morrey spaces based on the results of Lebesgue space with variable exponent as the infimum of exponent function p(·) equals 1. The corresponding commutators generated by BMO and Lipschitz functions are considered, respectively.

scholarly journals BMO Functions Generated by A X ℝ n Weights on Ball Banach Function Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Ruimin Wu ◽  
Songbai Wang
Keyword(s):  
Linear Operator ◽  
Function Space ◽  
Maximal Function ◽  
Lebesgue Space ◽  
Variable Exponent ◽  
Banach Function Space ◽  
Function Spaces ◽  
Banach Function Spaces ◽  
Bmo Functions ◽  
Littlewood Maximal Function

Let X be a ball Banach function space on ℝ n . We introduce the class of weights A X ℝ n . Assuming that the Hardy-Littlewood maximal function M is bounded on X and X ′ , we obtain that BMO ℝ n = α ln ω : α ≥ 0 , ω ∈ A X ℝ n . As a consequence, we have BMO ℝ n = α ln ω : α ≥ 0 , ω ∈ A L p · ℝ n ℝ n , where L p · ℝ n is the variable exponent Lebesgue space. As an application, if a linear operator T is bounded on the weighted ball Banach function space X ω for any ω ∈ A X ℝ n , then the commutator b , T is bounded on X with b ∈ BMO ℝ n .

scholarly journals Modular Uniform Convexity of Lebesgue Spaces of Variable Integrability

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 708 ◽  
Author(s):  
Mostafa Bachar ◽  
Osvaldo Mendez ◽  
Messaoud Bounkhel
Keyword(s):  
Fixed Point ◽  
Lebesgue Space ◽  
Variable Exponent ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Uniform Convexity ◽  
Convexity Property ◽  
Lebesgue Spaces ◽  
Central Result ◽  
Variable Integrability

We analyze the modular geometry of the Lebesgue space with variable exponent, L p ( · ) . Our central result is that L p ( · ) possesses a modular uniform convexity property. Part of the novelty is that the property holds even in the case sup x ∈ Ω p ( x ) = ∞ . We present specific applications to fixed point theory.

scholarly journals On Variable Exponent Amalgam Spaces

2012 ◽  
Vol 20 (3) ◽  
pp. 5-20 ◽  
Author(s):  
İsmail Aydin
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Weighted Lebesgue Space ◽  
Lebesgue Spaces ◽  
Wiener Amalgam Spaces ◽  
Local Component ◽  
Variable Exponent Lebesgue Space ◽  
New Family ◽  
Amalgam Spaces ◽  
Weighted Variable

Abstract We derive some of the basic properties of weighted variable exponent Lebesgue spaces Lp(.)w (ℝn) and investigate embeddings of these spaces under some conditions. Also a new family of Wiener amalgam spaces W(Lp(.)w ;Lqv) is defined, where the local component is a weighted variable exponent Lebesgue space Lp(.)w (ℝn) and the global component is a weighted Lebesgue space Lqv (ℝn) : We investigate the properties of the spaces W(Lp(.)w ;Lqv): We also present new Hölder-type inequalities and embeddings for these spaces.

scholarly journals Variable exponent fractional integrals in the limiting case α(x)p(n) ≡ n on quasimetric measure spaces

2020 ◽  
Vol 27 (1) ◽  
pp. 157-164
Author(s):  
Stefan Samko
Keyword(s):  
Growth Condition ◽  
Lebesgue Space ◽  
Measure Space ◽  
Variable Exponent ◽  
Fractional Integrals ◽  
Variable Order ◽  
Fractional Operator ◽  
Open Set ◽  
Measure Spaces ◽  
Limiting Case

AbstractWe show that the fractional operator {I^{\alpha(\,\cdot\,)}}, of variable order on a bounded open set in Ω, in a quasimetric measure space {(X,d,\mu)} in the case {\alpha(x)p(x)\equiv n} (where n comes from the growth condition on the measure μ), is bounded from the variable exponent Lebesgue space {L^{p(\,\cdot\,)}(\Omega)} into {\mathrm{BMO}(\Omega)} under certain assumptions on {p(x)} and {\alpha(x)}.

Variable-Exponent Lebesgue-Space Inversion for Brain Stroke Microwave Imaging

2020 ◽  
Vol 68 (5) ◽  
pp. 1882-1895 ◽  
Author(s):  
Igor Bisio ◽  
Claudio Estatico ◽  
Alessandro Fedeli ◽  
Fabio Lavagetto ◽  
Matteo Pastorino ◽  
...  
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Microwave Imaging ◽  
Variable Exponent Lebesgue Space ◽  
Brain Stroke ◽  
Space Inversion
Sign in / Sign up

Export Citation Format

Share Document