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A T1 theorem and Calderón–Zygmund operators in Campanato spaces on domains

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1 Published in 2019 at "Mathematische Nachrichten"

DOI: 10.1002/mana.201700488

Abstract: Given a Lipschitz domain D⊂Rd , a Calderón–Zygmund operator T and a modulus of continuity ω(x) , we solve the problem when the truncated operator TDf=T(fχD)χD sends the Campanato space Cω(D) into itself. The solution… read more here.

Keywords: theorem calder; calder; calder zygmund; zygmund operators ... See more keywords

An Endpoint Weak-Type Estimate for Multilinear Calderón–Zygmund Operators

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1 Published in 2019 at "Journal of Fourier Analysis and Applications"

DOI: 10.1007/s00041-019-09676-y

Abstract: The purpose of this article is to provide an alternative proof of the weak-type $$\left( 1,\ldots ,1;\frac{1}{m}\right) $$1,…,1;1m estimate for m-multilinear Calderón–Zygmund operators on $${\mathbb {R}}^n$$Rn first proved by Grafakos and Torres. Subsequent proofs in… read more here.

Keywords: weak type; calder zygmund; zygmund operators; estimate ... See more keywords

Nonlinear Calderón–Zygmund inequalities for maps

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1 Published in 2017 at "Annals of Global Analysis and Geometry"

DOI: 10.1007/s10455-018-9605-5

Abstract: Being motivated by the problem of deducing $$\mathsf {L}^{p}$$Lp-bounds on the second fundamental form of an isometric immersion from $$\mathsf {L}^{p}$$Lp-bounds on its mean curvature vector field, we prove a nonlinear Calderón–Zygmund inequality for maps… read more here.

Keywords: nonlinear calder; zygmund inequalities; calder zygmund; inequalities maps ... See more keywords

Vector-valued maximal multilinear Calderón–Zygmund operator with nonsmooth kernel on weighted Morrey space

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0 Published in 2017 at "Journal of Pseudo-Differential Operators and Applications"

DOI: 10.1007/s11868-016-0169-5

Abstract: In this paper, vector-valued Maximal multilinear Calderón–Zygmund operator with nonsmooth kernel and its commutators generated by $$\textit{BMO}$$BMO function are studied. The purpose of this paper is to establish that these operators are bounded on certain… read more here.

Keywords: zygmund operator; calder zygmund; vector valued;

Boundedness of Calderón–Zygmund operators on special John–Nirenberg–Campanato and Hardy-type spaces via congruent cubes

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0 Published in 2021 at "Analysis and Mathematical Physics"

DOI: 10.1007/s13324-021-00626-w

Abstract: Abstract Let p ∈ [1,∞], q ∈ (1,∞), s ∈ Z+ := N∪{0}, and α ∈ R. In this article, the authors introduce a reasonable version T̃ of the Calderón–Zygmund operator T on JN (p,q,s)α… read more here.

Keywords: special john; congruent cubes; nirenberg campanato; john nirenberg ... See more keywords

Maximal and Calderón–Zygmund operators on the local variable Morrey–Lorentz spaces and some applications

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0 Published in 2021 at "Applicable Analysis"

DOI: 10.1080/00036811.2021.1952995

Abstract: In this paper, we give the definition of local variable MorreyLorentz spaces Mloc p(·),q(·),λ(R n) which are a new class of functions. Also, we prove the boundedness of the Hardy-Littlewood maximal operator M and Calderón-Zygmund… read more here.

Keywords: calder zygmund; zygmund operators; local variable; calder ... See more keywords

The Higher Integrability of Commutators of Calderón-Zygmund Singular Integral Operators on Differential Forms

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0 Published in 2018 at "Journal of Function Spaces"

DOI: 10.1155/2018/1949747

Abstract: In this article, the higher integrability of commutators of Calderón-Zygmund singular integral operators on differential forms is derived. Also, the higher order Poincaré-type inequalities for the commutators acting on the solutions of Dirac-harmonic equations are… read more here.

Keywords: calder zygmund; zygmund singular; commutators calder; integrability commutators ... See more keywords

Weighted norm inequality for bilinear Calderón–Zygmund operators on Herz–Morrey spaces with variable exponents

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0 Published in 2019 at "Journal of Inequalities and Applications"

DOI: 10.1186/s13660-019-2202-8

Abstract: In this paper, we obtain a weighted norm inequality of bilinear Calderón–Zygmund operators in Herz–Morrey spaces with variable exponents and weight in the variable Muckenhoupt class. read more here.

Keywords: weighted norm; bilinear calder; calder zygmund; zygmund operators ... See more keywords

On weighted compactness of commutators of bilinear maximal Calderón–Zygmund singular integral operators

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1 Published in 2022 at "Forum Mathematicum"

DOI: 10.1515/forum-2020-0357

Abstract: Abstract Let T be a bilinear Calderón–Zygmund singular integral operator and let T*{T^{*}} be its corresponding truncated maximal operator. For any b∈BMO⁡(ℝn){b\in\operatorname{BMO}({\mathbb{R}^{n}})} and b→=(b1,b2)∈BMO⁡(ℝn)×BMO⁡(ℝn){\vec{b}=(b_{1},b_{2})\in\operatorname{BMO}({\mathbb{R}^{n}})\times% \operatorname{BMO}({\mathbb{R}^{n}})}, let Tb,j*{T^{*}_{b,j}} (j=1,2{j=1,2}) and Tb→*{T^{*}_{\vec{b}}} be the commutators in the… read more here.

Keywords: operatorname; mathbb; bmo; vec ... See more keywords

Calderón-Zygmund operators on Lipschitz spaces over RD spaces

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0 Published in 2020 at "Quaestiones Mathematicae"

DOI: 10.2989/16073606.2019.1709579

Abstract: Abstract. Suppose that (X, d, µ) is a metric measure space of homogeneous type in the sense of Coifman and Weiss with a reverse doubling condition. By establishing the Littlewood-Paley characterization of Lipschitz spaces, a… read more here.

Keywords: zygmund; calder zygmund; zygmund operators; lipschitz spaces ... See more keywords