scholarly journals Polynomial Inequalities in Regions with Piecewise Asymptotically Conformal Curve in the Weighted Lebesgue Space

2018 ◽  
Vol 3 (2) ◽  
pp. 100-112
Author(s):  
F.G. ABDULLAYEV ◽  
◽  
D. SIMSEK ◽  
N. SAYPIDINOVA ◽  
Z. TASHPAEVA ◽  
...  
Keyword(s):  
Lebesgue Space ◽  
Weighted Lebesgue Space ◽  
Polynomial Inequalities ◽  
Asymptotically Conformal Curve

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.

scholarly journals Polynomial inequalities in Lavrentiev regions with interior and exterior zero angles in the weighted Lebesgue space

2016 ◽  
Vol 100 (114) ◽  
pp. 209-227 ◽  
Author(s):  
F.G. Abdullayev ◽  
N.P. Özkartepe
Keyword(s):  
Lebesgue Space ◽  
Weighted Lebesgue Space ◽  
Algebraic Polynomials ◽  
Polynomial Inequalities

We study estimation of the modulus of algebraic polynomials in the bounded and unbounded regions with piecewise-quasismooth boundary, having interior and exterior zero angles, in the 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.

scholarly journals On a measure of non-compactness for singular integrals

2003 ◽  
Vol 1 (1) ◽  
pp. 35-43 ◽  
Author(s):  
Alexander Meskhi
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Lebesgue Space ◽  
Singular Integrals ◽  
Weighted Lebesgue Space ◽  
Smooth Curves

It is proved that there exists no weight pair(v, w)for which a singular integral operator is compact from the weighted Lebesgue spaceLwp(Rn)toLvp(Rn). Moreover, a measure of non-compatness for this operator is estimated from below. Analogous problems for Cauchy singular integrals defined on Jordan smooth curves are studied.

scholarly journals On Solvability of the Sonin–Abel Equation in the Weighted Lebesgue Space

2021 ◽  
Vol 5 (3) ◽  
pp. 77
Author(s):  
Maksim V. Kukushkin
Keyword(s):  
Convolution Operator ◽  
Lebesgue Space ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Abel Equation ◽  
Weighted Lebesgue Space ◽  
Power Type ◽  
Uniqueness Of The Solution ◽  
Logarithmic Singularities ◽  
The Right

In this paper we present a method of studying a convolution operator under the Sonin conditions imposed on the kernel. The particular case of the Sonin kernel is a kernel of the fractional integral Riemman–Liouville operator, other various types of the Sonin kernels are a Bessel-type function, functions with power-logarithmic singularities at the origin e.t.c. We pay special attention to study kernels close to power type functions. The main our aim is to study the Sonin–Abel equation in the weighted Lebesgue space, the used method allows us to formulate a criterion of existence and uniqueness of the solution and classify a solution, due to the asymptotics of the Jacobi series coefficients of the right-hand side.

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