The basis property of the Legendre polynomials in the variable exponent Lebesgue space $ L^{p(x)}(-1,1)$

2009 ◽  
Vol 200 (1) ◽  
pp. 133-156 ◽  
Author(s):  
Idris I Sharapudinov
Keyword(s):  
Lebesgue Space ◽  
Legendre Polynomials ◽  
Variable Exponent ◽  
Basis Property ◽  
Variable Exponent Lebesgue Space

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 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.

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.

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