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 Неравенство Бернштейна - Никольского в весовых пространствах Лебега

2020 ◽  
Author(s):  
H.H. Bang ◽  
V. N. Huy
Keyword(s):  
Lebesgue Space ◽  
Dimensional Case ◽  
Weighted Lebesgue Space ◽  
Lebesgue Spaces ◽  
Measurable Functions ◽  
Weighted Lebesgue Spaces ◽  
Right Hand ◽  
Nikol’Skii Inequality ◽  
The Right

In this paper, we give some results concerning Bernstein--Nikol'skii inequality for weighted Lebesgue spaces. The main result is as follows: Let $1 < u,p < \infty$, $0<q+ 1/p <v + 1/u <1,$ $v-q\geq 0$, $\kappa >0$, $f \in L^u_v(\R)$ and $\supp\widehat{f} \subset [-\kappa, \kappa]$. Then $D^mf \in L^p_q(\R)$, $\supp\widehat{D^m f}=\supp\widehat{f}$ and there exists a~constant~$C$ independent of $f$, $m$, $\kappa$ such that $\|D^mf\|_{L^p_{q}} \leq C m^{-\varrho} \kappa^{m+\varrho} \|f\|_{ L^u_v}, $ for all $m = 1,2,\dots $, where $\varrho=v + \frac{1}{u} -\frac{1}{p} - q>0,$ and the weighted Lebesgue space $L^p_q$ consists of all measurable functions such that $\|f\|_{L^p_q} = \big(\int_{\R} |f(x)|^p |x|^{pq} dx\big)^{1/p} < \infty.$ Moreover, $ \lim_{m\to \infty}\|D^mf\|_{L^p_{q}}^{1/m}= \sup \big\{ |x|: \, x \in \textnormal{supp}\widehat{f}\big \}.$ The~advantage of our result is that $m^{-\varrho}$ appears on the right hand side of the inequality ($\varrho >0$), which has never appeared in related articles by other authors. The corresponding result for the $n$-dimensional case is also obtained.

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

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.

A New Composite Quadrature Rule

2013 ◽  
Vol 5 (04) ◽  
pp. 595-606
Author(s):  
Weiwei Sun ◽  
Qian Zhang
Keyword(s):  
Boundary Conditions ◽  
Orthogonal Polynomials ◽  
Quadrature Rule ◽  
Numerical Results ◽  
Weight Functions

AbstractWe present a new composite quadrature rule which is exact for polynomials of degree 2N+K– 1 withNabscissas at each subinterval andKboundary conditions. The corresponding orthogonal polynomials are introduced and the analytic formulae for abscissas and weight functions are presented. Numerical results show that the new quadrature rule is more efficient, compared with classical ones.

Complex Weight Functions for Classical Orthogonal Polynomials

1991 ◽  
Vol 43 (6) ◽  
pp. 1294-1308 ◽  
Author(s):  
Mourad E. H. Ismail ◽  
David R. Masson ◽  
Mizan Rahman
Keyword(s):  
Orthogonal Polynomials ◽  
Weight Functions ◽  
Classical Orthogonal Polynomials ◽  
The Real ◽  
Complex Functions ◽  
Wilson Polynomials ◽  
Distributional Weight

AbstractWe give complex weight functions with respect to which the Jacobi, Laguerre, little q-Jacobi and Askey-Wilson polynomials are orthogonal. The complex functions obtained are weight functions in a wider range of parameters than the real weight functions. They also provide an alternative to the recent distributional weight functions of Morton and Krall, and the more recent hyperfunction weight functions of Kim.

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