Boundedness of rough singular integral operatorson the homogeneous Morrey-Herz spaces

Lu, Shanzhen; Xu, Luoshan

doi:10.14492/hokmj/1285766224

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Introduction4

Preliminaries and Main Lemmas1

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Cited by 50 publications

(30 citation statements)

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“…In 1962, Benedek, Calderón and Panzone showed that if Ω ∈ C 1 (S n−1 ), then μ Ω is of type (p, p)(1 < p < ∞). In [4] , Chen Definition 1.1 [6] . Let α ∈ R, 0 < p ≤ ∞, 0 < q < ∞ and λ ≥ 0.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Cbmo estimates for Marcinkiewicz integrals on homogeneous Morrey-Herz spaces

2008

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Cbmo estimates for Marcinkiewicz integrals on homogeneous Morrey-Herz spaces

2008

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“…More results and further details can be found in [26][27][28]. On the basis of above available results, the theory of the homogeneous Morrey-Herz spaces goes back to Lu-Xu [29] who considered the boundedness of a class of sublinear operators; also see [6,30,31] for more further results.…”

Section: Preliminaries and Main Lemmasmentioning

confidence: 99%

Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces

Yang

Tao

2017

Journal of Function Spaces

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Let be the singular integral operator with variable kernel defined by ( ) = p.v. ∫ R (Ω( , − )/| − | ) ( )d and let (0 ≤ ≤ 1) be the fractional differentiation operator. Let * and ♯ be the adjoint of and the pseudoadjoint of , respectively. In this paper, the authors prove that − and ( * − ♯ ) are bounded, respectively, from Morrey-Herz spaceṡ, ,1 (R ) to the weak Morrey-Herz spaceṡ, ,1 (R ) by using the spherical harmonic decomposition. Furthermore, several norm inequalities for the product 1 2 and the pseudoproduct 1 ∘ 2 are also given.

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“…The complete theory of Herz spaces for the case of general indexes was established by ; see [4]. Recently, Lu and Xu defined the homogeneous Morrey-Herz spaces in [5].…”

Section: Introductionmentioning

confidence: 99%

Morrey Meets Herz with Variable Exponent and Applications to Commutators of Homogeneous Fractional Integrals with Rough Kernels

Wang¹,

Wang²,

Fu³

2017

Journal of Function Spaces

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We define the new central Morrey space with variable exponent and investigate its relation to the Morrey-Herz spaces with variable exponent. As applications, we obtain the boundedness of the homogeneous fractional integral operator Ω, and its commutator [ , Ω, ] on Morrey-Herz space with variable exponent, where Ω ∈ (S −1 ) for ≥ 1 is a homogeneous function of degree zero, 0 < < , and is a BMO function.

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Boundedness of rough singular integral operatorson the homogeneous Morrey-Herz spaces

Cited by 50 publications

References 4 publications

Cbmo estimates for Marcinkiewicz integrals on homogeneous Morrey-Herz spaces

Cbmo estimates for Marcinkiewicz integrals on homogeneous Morrey-Herz spaces

Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces

Morrey Meets Herz with Variable Exponent and Applications to Commutators of Homogeneous Fractional Integrals with Rough Kernels

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