Geodesic
On the Regularity of the Multisublinear Maximal Functions
Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 808-817

Voir la notice de l'article provenant de la source Cambridge University Press

This paper is concerned with the study of the regularity for the multisublinear maximal operator. It is proved that the multisublinear maximal operator is bounded on first-order Sobolev spaces. Moreover, two key point-wise inequalities for the partial derivatives of the multisublinear maximal functions are established. As an application, the quasi-continuity on the multisublinear maximal function is also obtained.
DOI : 10.4153/CMB-2014-070-7
Mots-clés : 42B25, 46E35, regularity, multisublinear maximal operator, Sobolev spaces, partial derivative, quasicontinuity 
Liu, Feng; Wu, Huoxiong. On the Regularity of the Multisublinear Maximal Functions. Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 808-817. doi: 10.4153/CMB-2014-070-7
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[1] [1] Aldaz, J. M. and J. Pérez Lâzaro, Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities. Trans. Amer. Math. Soc. 359(2007), no. 5, 2443–2461. http://dx.doi.Org/10.1090/S0002-9947-06-04347-9 Google Scholar

[2] [2] Carneiro, E. and Moreira, D., On the regularity of maximal operators. Proc. Amer. Math. Soc. 136(2008), no. 12, 4395–4404. http://dx.doi.Org/10.1090/S0002-9939-08-09515-4 Google Scholar

[3] [3] Fédérer, H. and Ziemer, W., The Lebesgue set of a function whose distribution derivatives are p-th power summable. Indiana Univ. Math. J. 22(1972/73), 139–158. http://dx.doi.Org/10.1512/iumj.1973.22.22013 Google Scholar

[4] [4] Gilbarg, D. and Trudinger, N. S., Elliptic partial differential equations of second order. Second éd., Grundlehren der Mathematischen Wissenschaften, 224, Springer-Verlag, Berlin, 1983. Google Scholar

[5] [5] Hajlasz, P. and Onninen, J., On boundedness of maximal functions in Sobolev spaces. Ann. Acad. Sci. Fenn. Math. 29(2004), no. 1,167-176. Google Scholar

[6] [6] Kinnunen, J., The Hardy-Littlewood maximal function of a Sobolev function. Israel J. Math. 100(1997), 117–124. http://dx.doi.Org/10.1007/BF02773636 Google Scholar

[7] [7] Kinnunen, J. and Lindqvist, P., The derivative of the maximal function. J. Reine. Angew. Math. 503(1998), 161–167. Google Scholar

[8] [8] Kinnunen, J. and Saksman, E., Regularity of the fractional maximal function. Bull. London Math. Soc. 35(2003), no. 4, 529–535. http://dx.doi.Org/10.1112/S0024609303002017 Google Scholar

[9] [9] Kurka, O., On the variation of the Hardy-Littlewood maximal function. arxiv:1210.0496v1 Google Scholar

[10] [10] Luiro, H., Continuity of the maximal operator in Sobolev spaces. Proc. Amer. Math. Soc. 135(2007), no. 1, 243–251. http://dx.doi.Org/10.1090/S0002-9939-06-08455-3 Google Scholar

[11] [11] Tanaka, H., A remark on the derivative of the one-dimensional Hardy-Littlewood maximal function. Bull. Austral. Math. Soc. 65(2002), no. 2, 253–258. http://dx.doi.Org/10.1017/S0004972700020293 Google Scholar

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