scholarly journals On the Calderon-Zygmund singular integral operators and local Hardy-type amalgam spaces (part 2)

2021 ◽  
Vol 16 (2) ◽  
pp. 61-77
Author(s):  
Hon Ming Ho
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Hardy Type ◽  
Amalgam Spaces

scholarly journals Boundedness of Singular Integrals on Hardy Type Spaces Associated with Schrödinger Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jianfeng Dong ◽  
Jizheng Huang ◽  
Heping Liu
Keyword(s):  
Molecular Characterization ◽  
Singular Integral ◽  
Maximal Function ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Hardy Type ◽  
Type Spaces ◽  
Reverse Hölder

LetL=-Δ+Vbe a Schrödinger operator onRn,n≥3, whereV≢0is a nonnegative potential belonging to the reverse Hölder classBn/2. The Hardy type spacesHLp, n/(n+δ) <p≤1,for someδ>0, are defined in terms of the maximal function with respect to the semigroup{e-tL}t>0. In this paper, we investigate the bounded properties of some singular integral operators related toL, such asLiγand∇L-1/2, on spacesHLp. We give the molecular characterization ofHLp, which is used to establish theHLp-boundedness of singular integrals.

Boundedness of operators of Hardy type in ΛP,q spaces and weighted mixed inequalities for singular integral operators

1997 ◽  
Vol 127 (1) ◽  
pp. 157-170 ◽  
Author(s):  
F. J. Martín-Reyes ◽  
P. Ortega Salvador ◽  
M. D. Sarrión Gavilán
Keyword(s):  
Singular Integral ◽  
Singular Integrals ◽  
Weak Type ◽  
Integral Operators ◽  
Lorentz Spaces ◽  
Singular Integral Operators ◽  
Hardy Type

We consider certain n-dimensional operators of Hardy type and we study their boundedness in These spaces were introduced by M. J. Carro and J. Soria and include weighted Lp, q spaces and classical Lorentz spaces. As an application, we obtain mixed weak-type inequalities for Calderón—Zygmund singular integrals, improving results due to K. Andersen and B. Muckenhoupt.

scholarly journals Commutators of Singular Integral Operators and Lipschitz Functions on Amalgam Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Jiao Ma ◽  
Zongguang Liu
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lipschitz Functions ◽  
Amalgam Spaces

In this paper, we obtain the boundedness of commutators generated by singular integral operators and Lipschitz functions on amalgam spaces and weighted amalgam spaces.

scholarly journals On the Multilinear Singular Integrals and Commutators in the Weighted Amalgam Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Feng Liu ◽  
Huoxiong Wu ◽  
Daiqing Zhang
Keyword(s):  
Singular Integral ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Norm Inequalities ◽  
Norm Estimates ◽  
Multilinear Singular Integral ◽  
Bmo Functions ◽  
Amalgam Spaces ◽  
Multilinear Singular Integrals

This paper is concerned with the norm estimates for the multilinear singular integral operators and their commutators formed by BMO functions on the weighted amalgam spacesLvw→q,Lpαℝn. Some criterions of boundedness for such operators inLvw→q,Lpαℝnare given. As applications, the norm inequalities for the multilinear Calderón-Zygmund operators and multilinear singular integrals with nonsmooth kernels as well as the corresponding commutators onLvw→q,Lpαℝnare obtained.

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.

scholarly journals The Calderón–Zygmund Theorem with an $$L^1$$ Mean Hörmander Condition

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Soichiro Suzuki
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Acta Math ◽  
Limited Range ◽  
Singular Integral Operators ◽  
Convolution Type ◽  
Worst Case ◽  
Hörmander Condition

AbstractIn 2019, Grafakos and Stockdale introduced an $$L^q$$ L q mean Hörmander condition and proved a “limited-range” Calderón–Zygmund theorem. Comparing their theorem with the classical one, it requires weaker assumptions and implies the $$L^p$$ L p boundedness for the “limited-range” instead of $$1< p < \infty $$ 1 < p < ∞ . However, in this paper, we show that the $$L^q$$ L q mean Hörmander condition is actually enough to obtain the $$L^p$$ L p boundedness for all $$1< p < \infty $$ 1 < p < ∞ even in the worst case $$q=1$$ q = 1 . We use a similar method to that used by Fefferman (Acta Math 124:9–36, 1970): form the Calderón–Zygmund decomposition with the bounded overlap property and approximate the bad part. Also we give a criterion of the $$L^2$$ L 2 boundedness for convolution type singular integral operators under the $$L^1$$ L 1 mean Hörmander condition.

Sign in / Sign up

Export Citation Format

Share Document