The Basis Property of Ultraspherical Jacobi Polynomials in a Weighted Lebesgue Space with Variable Exponent

2019 ◽  
Vol 106 (3-4) ◽  
pp. 616-638
Author(s):  
I. I. Sharapudinov
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Jacobi Polynomials ◽  
Basis Property ◽  
Weighted 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.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document