scholarly journals Pointwise estimates of one-sided approximations of one class of singular integrals

2013 ◽  
Vol 21 ◽  
pp. 141
Author(s):  
A.M. Pas'ko ◽  
O.O. Kolesnyk
Keyword(s):  
Singular Integrals ◽  
Algebraic Polynomials ◽  
Pointwise Estimates ◽  
Pointwise Estimation

The pointwise estimation of the approximation to the class ${\breve{W}}_{\infty}^r$, $r \geqslant 1$, by algebraic polynomials is established.

scholarly journals Pointwise estimates for commutator singular integrals

1978 ◽  
Vol 62 (1) ◽  
pp. 1-15 ◽  
Author(s):  
B. Baishanski ◽  
R. Coifman
Keyword(s):  
Singular Integrals ◽  
Pointwise Estimates

scholarly journals Weighted Estimates for Maximal Commutators of Multilinear Singular Integrals

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Dongxiang Chen ◽  
Suzhen Mao
Keyword(s):  
Linear Operator ◽  
Lipschitz Function ◽  
Singular Integrals ◽  
Pointwise Estimates ◽  
Multilinear Commutator ◽  
Weighted Lipschitz Function ◽  
Weighted Estimates ◽  
Sharp Function ◽  
Multilinear Commutators ◽  
Multilinear Singular Integrals

This paper is concerned with the pointwise estimates for the sharp function of the maximal multilinear commutatorsTΣb*and maximal iterated commutatorTΠb*, generalized bym-linear operatorTand a weighted Lipschitz functionb. The(Lp1(μ)×⋯×Lpm(μ),Lr(μ1-r))boundedness and the(Lp1(μ)×⋯×Lpm(μ),Lr(μ1-mr))boundedness are obtained for maximal multilinear commutatorTΣb*and maximal iterated commutatorTΠb*, respectively.

POINTWISE ESTIMATE OF DEVIATION OF KRIAKIN POLYNOMIAL FROM A FUNCTION, CONTINUOUS ON A SEGMENT

2019 ◽  
pp. 12-14
Author(s):  
M. Shchehlov
Keyword(s):  
Pointwise Estimate ◽  
Algebraic Polynomials ◽  
Pointwise Estimates

New estimates for the algebraic polynomials that approximate a function continuous on a segment involving moduli of continuous of high orders are obtained, namely the pointwise estimates.

scholarly journals Pointwise estimates of the best one-sided approximations of classes $$$W^r_{\infty}$$$ for $$$0 < r < 1$$$

2018 ◽  
Vol 26 (1) ◽  
pp. 62
Author(s):  
A.M. Pas'ko ◽  
V.D. Stefura
Keyword(s):  
Pointwise Estimates ◽  
Pointwise Estimation

The asymptotic pointwise estimation of the best one-sided approximations to the classes $$$W^r_{\infty}$$$, $$$0 < r < 1$$$, has been established.

scholarly journals One-sided approximation of some classes of singular integrals with regard to point position on the interval

2021 ◽  
Vol 16 ◽  
pp. 117
Author(s):  
A.M. Pasko
Keyword(s):  
Singular Integrals ◽  
Algebraic Polynomials ◽  
Approximation Of Functions ◽  
Point Position

We obtain asymptotically exact estimates of approximation of functions from some classes of singular integrals by algebraic polynomials with regard to point position on the interval.

scholarly journals Uniform and pointwise estimates for algebraic polynomials in regions with interior and exterior zero angles

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 403-413
Author(s):  
Özkartepe Pelin ◽  
Tuncay Tunç ◽  
Fahreddin Abdullayev
Keyword(s):  
Piecewise Smooth ◽  
Algebraic Polynomials ◽  
Pointwise Estimates ◽  
Smooth Curves

In this study, we give some estimates on the Nikolskii-type inequalities for complex algebraic polynomials in regions with piecewise smooth curves having exterior and interior zero angles.

Multi-parameter Singular Integrals II: General Theory

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
General Theory ◽  
Singular Integral ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Main Issue

This chapter turns to a general theory which generalizes and unifies all of the examples in the preceding chapters. A main issue is that the first definition from the trichotomy does not generalize to the multi-parameter situation. To deal with this, strengthened cancellation conditions are introduced. This is done in two different ways, resulting in four total definitions for singular integral operators (the first two use the strengthened cancellation conditions, while the later two are generalizations of the later two parts of the trichotomy). Thus, we obtain four classes of singular integral operators, denoted by A1, A2, A3, and A4. The main theorem of the chapter is A1 = A2 = A3 = A4; i.e., all four of these definitions are equivalent. This leads to many nice properties of these singular integral operators.

The Calder´on-Zygmund Theory I: Ellipticity

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
Classical Theory ◽  
Singular Integral ◽  
Singular Integrals ◽  
Differential Operators ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Single Parameter ◽  
Partial Differential ◽  
Translation Invariant ◽  
Partial Differential Operators

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

Sign in / Sign up

Export Citation Format

Share Document