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.

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

Singular Integrals in Weighted Lebesgue Spaces with Variable Exponent

2003 ◽  
Vol 10 (1) ◽  
pp. 145-156 ◽  
Author(s):  
V. Kokilashvili ◽  
S. Samko
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Weighted Space ◽  
Singular Integrals ◽  
Power Weight ◽  
Weighted Lebesgue Space ◽  
Lebesgue Spaces ◽  
Dini Condition ◽  
Zygmund Operator ◽  
Weighted Lebesgue Spaces

Abstract In the weighted Lebesgue space with variable exponent the boundedness of the Calderón–Zygmund operator is established. The variable exponent 𝑝(𝑥) is assumed to satisfy the logarithmic Dini condition and the exponent β of the power weight ρ(𝑥) = |𝑥 – 𝑥0| β is related only to the value 𝑝(𝑥0). The mapping properties of Cauchy singular integrals defined on the Lyapunov curve and on curves of bounded rotation are also investigated within the framework of the above-mentioned weighted space.

Singular integral operators in some variable exponent Lebesgue spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Mieczysław Mastyło ◽  
Alexander Meskhi
Keyword(s):  
Singular Integral ◽  
Lebesgue Space ◽  
Variable Exponent ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Space ◽  
Variable Exponent Lebesgue Spaces ◽  
Cauchy Singular Integral

AbstractThe paper deals with the exploration of those subclasses of the variable exponent Lebesgue space {L^{p(\,\cdot\,)}} with {\min p(\,\cdot\,)=1}, which are invariant with respect to Cauchy singular integral operators.

scholarly journals Weighted variable exponent amalgam spaces $W(L^{p(x)},L_w^q)$

2012 ◽  
Vol 47 (1) ◽  
pp. 165-174 ◽  
Author(s):  
Ismail Aydin ◽  
A. Turan Gürkanli
Keyword(s):  
Variable Exponent ◽  
Amalgam Spaces ◽  
Weighted Variable

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.

Polynomial inequalities in regions with corners in theweighted Lebesgue spaces

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5647-5670 ◽  
Author(s):  
Fahreddin Abdullayev
Keyword(s):  
Orthogonal Polynomials ◽  
Lebesgue Space ◽  
Weight Functions ◽  
Weighted Lebesgue Space ◽  
Algebraic Polynomials ◽  
Lebesgue Spaces ◽  
Polynomial Inequalities

In this work, we investigate the order of the growth of the modulus of orthogonal polynomials over a contour and also arbitrary algebraic polynomials in regions with corners in a weighted Lebesgue space, where the singularities of contour and the weight functions satisfy some condition.

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