Singular Integrals and Related Topics

Lu, Shanzhen; Ding, Yong; Yan, Dunyan

doi:10.1142/6428

Cited by 113 publications

(76 citation statements)

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“…Since Stein's work in 1958, the continuity of Marcinkiewicz integral has been extensively studied as a research topic and also provides useful tools in harmonic analysis [32,40,42,44].…”

Section: Sublinear Operators and Commutators 349mentioning

confidence: 99%

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Boundedness of Sublinear Operators and Commutators on Generalized Morrey Spaces

Guliyev

Aliyev

Karaman

et al. 2011

Integr. Equ. Oper. Theory

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In this paper the authors study the boundedness for a large class of sublinear operators Tα, α ∈ [0, n) generated by Calderón-Zygmund operators (α = 0) and generated by Riesz potential operator (α > 0) on generalized Morrey spaces Mp,ϕ. As an application of the above result, the boundeness of the commutator of sublinear operators T b,α , α ∈ [0, n) on generalized Morrey spaces is also obtained. In the case b ∈ BM O and T b,α is a sublinear operator, we find the sufficient conditions on the pair (ϕ1, ϕ2) which ensures the boundedness of the operators T b,α , α ∈ [0, n) from one generalized Morrey space Mp,ϕ 1 to another Mq,ϕ 2 with 1/p − 1/q = α/n. In all the cases the conditions for the boundedness are given in terms of Zygmund-type integral inequalities on (ϕ1, ϕ2), which do not assume any assumption on monotonicity of ϕ1, ϕ2 in r. Conditions of these theorems are satisfied by many important operators in analysis, in particular, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.Mathematics Subject Classification (2010). Primary 42B20, 42B25, 42B35.

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“…Since Stein's work in 1958, the continuity of Marcinkiewicz integral has been extensively studied as a research topic and also provides useful tools in harmonic analysis [32,40,42,44].…”

Section: Sublinear Operators and Commutators 349mentioning

confidence: 99%

“…It is well known that fractional maximal operator, Riesz potential and Calderón-Zygmund operators play an important role in harmonic analysis (see [19,32,42,44]). …”

Section: Introductionmentioning

confidence: 99%

Boundedness of Sublinear Operators and Commutators on Generalized Morrey Spaces

Guliyev

Aliyev

Karaman

et al. 2011

Integr. Equ. Oper. Theory

View full text Add to dashboard Cite

show abstract

“…In particular, when p = 1, 1 < q < ∞, and α = 1 − 1/q, the space K α,p q (R n ) is A q (R n ), which is called to be the Beurling algebra introduced by Beurling [5] with a different but equivalent norm, and the spaces HK α,p q (R n ) and HK α,p q (R n ) are the space HA q (R n ) introduced by Chen and Lau [6] and García-Cuerva [7] and the space HK q (R n ) introduced by Lu and Yang [8] , respectively. In addition, more knowledge on Hardy spaces and Herz-type Hardy spaces can be found in, e.g., [9][10][11][12][13].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%