Regularity for commutators of the local multilinear fractional maximal operators

Xiao, Zhili; Liu, Feng

doi:10.1515/anona-2020-0162

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Introduction and Main Results1

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2024

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Cited by 3 publications

(1 citation statement)

References 30 publications

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“…where dH n−1 denotes the normalized (n-1)-dimensional Hausdorff measure, |∂B(x, r)| = n̟ n r n−1 , and ̟ n is the volume of the unit ball on R n . The further development about the regularity of maximal operators, we can see [2,5,12,13,14,15,17,18,21] and so on.…”

Section: Introduction and Main Resultsmentioning

confidence: 95%

Regularity for a class of local fractional new maximal operators

Shuang-ping

2023

Preprint

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This paper is devoted to studying the regularity properties for the new maximal operator Mϕ and the fractional new maximal operator Mϕ,β in the local case. Some new pointwise gradient estimates of Mϕ,Ω and Mϕ,β,Ω are given. Moreover, the boundedness of Mϕ,Ω and Mϕ,β,Ω on Sobolev space is established. As applications, we also obtained the bounds of the above operators on Sobolev space with zero boundary values MR(2010) Subject Classification 42B25, 46E35

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Section: Introduction and Main Resultsmentioning

confidence: 95%

Regularity for a class of local fractional new maximal operators

Shuang-ping

2023

Preprint

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Continuity and regularity for local multi-fractional new maximal operators

Li,

Tao

2024

Bulletin des Sciences Mathématiques

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Sobolev regularity for a class of local fractional new maximal operators

Li,

Tao

2024

Georgian Mathematical Journal

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This paper is devoted to studying the regularity properties for the new maximal operator M φ {M_{\varphi}} and the fractional new maximal operator M φ , β {M_{\varphi,\beta}} in the local case. Some new pointwise gradient estimates of M φ , Ω {M_{\varphi,\Omega}} and M φ , β , Ω {M_{\varphi,\beta,\Omega}} are given. Moreover, the boundedness of M φ , Ω {M_{\varphi,\Omega}} and M φ , β , Ω {M_{\varphi,\beta,\Omega}} on Sobolev space is established. As applications, we also obtain the bounds of the above operators on Sobolev space with zero boundary values.

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Regularity for commutators of the local multilinear fractional maximal operators

Cited by 3 publications

References 30 publications

Regularity for a class of local fractional new maximal operators

Regularity for a class of local fractional new maximal operators

Continuity and regularity for local multi-fractional new maximal operators

Sobolev regularity for a class of local fractional new maximal operators

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