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On the domain and range of the maximal operator

  • Alberto Fiorenza (a1) and Miroslav Krbec (a2)
Abstract
Abstract

We give a detailed survey, known and new results on the domain and the range of the maximal operator. In particular we employ the grand Lp spaces and logarithmic Lebesgue spaces.

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[CP] L. A. Caffarelli and I. Peral , On W1,p estimates of elliptic equations in divergence form, Comm. Pure Appl. Math., 51 (1998), 121.

[DS] R. A. DeVore and R. C. Sharpley , Maximal functions measuring smoothness, American Mathematical Society, Memoirs of the AMS vol. 47, 293 (1984).

[ET] D. E. Edmunds and H. Triebel , Logarithmic Sobolev spaces and their applications to spectral theory, Proc. London Math. Soc. (3), 71 (1995), 333371.

[F1] A. Fiorenza , A note on the spherical maximal function, Rend. Accad. Sci. Fis. Mat. Napoli, 65 (1987), 7783.

[FS1] N. Fusco and C. Sbordone , Higher integrability from reverse Jensen inequalities with different supports, Partial Differential Equations and the Calculus of Variations: Essays in Honor of Ennio De Giorgi, Progress in Non-linear Differential Equations and their Applications, Birkhaüser Boston Inc. (1989), pp. 541561.

[FS2] N. Fusco and C. Sbordone , Higher integrability of the gradient of minimizers of functionals with nonstandard growth conditions, Comm. Pure Appl. Math., 43 (1990), 673683.

[GCRF] J. Garcéıa-Cuerva and J. L. Rubio de Francia , Weighted Norm Inequalities and Related Topics, North Holland, Amsterdam, 1985.

[GIM] L. Greco , T. Iwaniec and G. Moscariello , Limits of the improved integrability of the volume forms, Indiana Univ. Math. J., 44 (1995), 305339.

[Gu] M. de Guzméan , Differentiation of Integrals in Rn, Lecture Notes in Math. vol. 481, Springer-Verlag, Berlin-Heidelberg-New York, 1975.

[IS] T. Iwaniec and C. Sbordone , On the integrability of the Jacobian under minimal hypothesis, Arch. Rat. Mech. Anal., 119 (1992), 129143.

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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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