On the regularity of the Hardy-Littlewood maximal operator on subdomains of ℝn

Hannes Luiro

doi:10.1017/S0013091507000867

Abstract

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We establish the continuity of the Hardy-Littlewood maximal operator on W1,p(Ω), where Ω ⊂ ℝn is an arbitrary subdomain and 1 < p < ∞. Moreover, boundedness and continuity of the same operator is proved on the Triebel-Lizorkin spaces Fps,q (Ω) for 1 < p,q < ∞ and 0 < s < 1.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Stempak, Krzysztof and Tao, Xiangxing 2014. Local Morrey and Campanato Spaces on Quasimetric Measure Spaces. Journal of Function Spaces, Vol. 2014, Issue. , p. 1.

Heikkinen, Toni Kinnunen, Juha Korvenpää, Janne and Tuominen, Heli 2015. Regularity of the local fractional maximal function. Arkiv för Matematik, Vol. 53, Issue. 1, p. 127.

LUIRO, Hannes and VÄHÄKANGAS, Antti V. 2016. Local maximal operators on fractional Sobolev spaces. Journal of the Mathematical Society of Japan, Vol. 68, Issue. 3,

LIU, FENG CHEN, TING and WU, HUOXIONG 2016. A NOTE ON THE ENDPOINT REGULARITY OF THE HARDY–LITTLEWOOD MAXIMAL FUNCTIONS. Bulletin of the Australian Mathematical Society, Vol. 94, Issue. 1, p. 121.

Carneiro, Emanuel and Madrid, José 2016. Derivative bounds for fractional maximal functions. Transactions of the American Mathematical Society, Vol. 369, Issue. 6, p. 4063.

LIU, FENG 2017. A REMARK ON THE REGULARITY OF THE DISCRETE MAXIMAL OPERATOR. Bulletin of the Australian Mathematical Society, Vol. 95, Issue. 1, p. 108.

Liu, Feng and Wu, HuoXiong 2017. Regularity of discrete multisublinear fractional maximal functions. Science China Mathematics, Vol. 60, Issue. 8, p. 1461.

Liu, Feng and Wu, Huoxiong 2017. Endpoint Regularity of Multisublinear Fractional Maximal Functions. Canadian Mathematical Bulletin, Vol. 60, Issue. 3, p. 586.

Liu, Feng and Wu, Huoxiong 2017. On the regularity of maximal operators supported by submanifolds. Journal of Mathematical Analysis and Applications, Vol. 453, Issue. 1, p. 144.

Luiro, Hannes and Vähäkangas, Antti V. 2017. Beyond Local Maximal Operators. Potential Analysis, Vol. 46, Issue. 2, p. 201.

Carneiro, Emanuel Madrid, José and Pierce, Lillian B. 2017. Endpoint Sobolev and BV continuity for maximal operators. Journal of Functional Analysis, Vol. 273, Issue. 10, p. 3262.

Pérez, Carlos Picon, Tiago Saari, Olli and Sousa, Mateus 2018. Regularity of maximal functions on Hardy–Sobolev spaces. Bulletin of the London Mathematical Society, Vol. 50, Issue. 6, p. 1007.

Liu, Feng and Xu, Lei 2018. Regularity of one-sided multilinear fractional maximal functions. Open Mathematics, Vol. 16, Issue. 1, p. 1556.

Liu, Feng 2018. Endpoint regularity of discrete multisublinear fractional maximal operators associated with ℓ 1 $\ell^{1}$ -balls. Journal of Inequalities and Applications, Vol. 2018, Issue. 1,

Liu, Feng 2018. On the regularity of one-sided fractional maximal functions. Mathematica Slovaca, Vol. 68, Issue. 5, p. 1097.

Liu, Feng and Xu, Lei 2018. A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal Function. Journal of Function Spaces, Vol. 2018, Issue. , p. 1.

Zhang, Daiqing 2019. Endpoint regularity of discrete multilinear fractional nontangential maximal functions. Advances in Difference Equations, Vol. 2019, Issue. 1,

Carneiro, Emanuel 2019. New Trends in Applied Harmonic Analysis, Volume 2. p. 69.

Liu, Feng Xue, Qingying and Zhang, Pu 2020. Regularity and continuity of commutators of the Hardy–Littlewood maximal function. Mathematische Nachrichten, Vol. 293, Issue. 3, p. 491.

Liu, Feng Xue, Qingying and Yabuta, Kôzô 2020. A Note on Endpoint Sobolev Regularity of a Class of Bilinear Maximal Functions. Results in Mathematics, Vol. 75, Issue. 1,

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Article contents

On the regularity of the Hardy-Littlewood maximal operator on subdomains of ℝn

Abstract

Keywords

MSC classification

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

On the regularity of the Hardy-Littlewood maximal operator on subdomains of ℝn

Abstract

Keywords

MSC classification

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