SOME INTEGRAL INEQUALITIES FOR QUASIMONOTONE FUNCTIONS IN WEIGHTED VARIABLE EXPONENT LEBESGUE SPACE WITH 0

2020 ◽  
Vol 11 (4) ◽  
pp. 58-65
Author(s):  
Abdelkader Senouci ◽  
◽  
Abdelkader Zanou ◽  
◽  
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Integral Inequalities ◽  
Variable Exponent Lebesgue Space ◽  
Weighted Variable

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.

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.

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

scholarly journals Modular Uniform Convexity of Lebesgue Spaces of Variable Integrability

2018 ◽  
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 ◽  
Variable Exponent Lebesgue Space ◽  
Variable Integrability

We analyze the modular geometry of the variable exponent Lebesgue space Lp(.). We show that Lp(.) possesses a modular uniform convexity property. Part of the novelty is that the property holds even in the case supp(x) = ∞ . We present specific applications to fixed point theory. xÆΩ

scholarly journals Local Characterizations of Besov and Triebel-Lizorkin Spaces with Variable Exponent

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Baohua Dong ◽  
Jingshi Xu
Keyword(s):  
Lebesgue Space ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Variable Exponent Lebesgue Space ◽  
Littlewood Maximal Operator

We introduce new Besov and Triebel-Lizorkin spaces with variable integrable exponent, which are different from those introduced by the second author early. Then we characterize these spaces by the boundedness of the local Hardy-Littlewood maximal operator on variable exponent Lebesgue space. Finally the completeness and the lifting property of these spaces are also given.

scholarly journals The Hardy--Littlewood maximal operator and BLO1/log class of exponents

2016 ◽  
Vol 23 (3) ◽  
pp. 393-398 ◽  
Author(s):  
Tengiz Kopaliani ◽  
Shalva Zviadadze
Keyword(s):  
Lebesgue Space ◽  
Maximal Operator ◽  
Variable Exponent ◽  
The Other ◽  
Variable Exponent Lebesgue Space ◽  
Other Hand ◽  
Littlewood Maximal Operator

AbstractIt is well known that if the Hardy–Littlewood maximal operator is bounded in the variable exponent Lebesgue space ${L^{p(\,\cdot\,)}[0;1]}$, then ${p(\,\cdot\,)\in\mathrm{BMO}^{1/\log}}$. On the other hand, there exists an exponent ${p(\,\cdot\,)\in\mathrm{BMO}^{1/\log}}$, ${1<p_{-}\leq p_{+}<\infty}$, such that the Hardy–Littlewood maximal operator is not bounded in ${L^{p(\,\cdot\,)}[0;1]}$. But for any exponent ${p(\,\cdot\,)\in\mathrm{BMO}^{1/\log}}$, ${1<p_{-}\leq p_{+}<\infty}$, there exists a constant ${c>0}$ such that the Hardy–Littlewood maximal operator is bounded in ${L^{p(\,\cdot\,)+c}[0;1]}$. In this paper, we construct an exponent ${p(\,\cdot\,)}$, ${1<p_{-}\leq p_{+}<\infty}$, ${1/p(\,\cdot\,)\in\mathrm{BLO}^{1/\log}}$ such that the Hardy–Littlewood maximal operator is not bounded in ${L^{p(\,\cdot\,)}[0;1]}$.

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