We consider the Marcinkiewicz function space MW and its subspace of order continuous elements M0W. We provide criteria for a function in the unit ball of MW or M0W to be a smooth point

Contact details are reproduced from the original publication and may be historical.

Anna Kamińska

Dept. of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, U.S.A.

kaminska@memphis.edu

Anca M. Parrish

Dept. of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, U.S.A.

abuican1@memphis.edu
  1. S. Banach: Theory of Linear Operations, North-Holland Mathematical Library 38, North-Holland, Amsterdam (1987).Google Scholar
  2. C. Bennett, R. Sharpley: Interpolation of Operators, Pure and Applied Mathematics 129, Academic Press, Boston (1988).Google Scholar
  3. S. Bian, H. Hudzik, T. Wang: Smooth, very smooth and strongly smooth points in Musielak-Orlicz sequence spaces, Bull. Aust. Math. Soc. 63(3) (2001) 441–457.https://doi.org/10.1017/S0004972700019523Google Scholar
  4. N. L. Carothers, R. Haydon, P. K. Lin: On the isometries of the Lorentz function spaces, Israel J. Math. 84(1–2) (1993) 265–287.https://doi.org/10.1007/BF02761703Google Scholar
  5. Sh. Chen, H. Hudzik, A. Kamińska: Support functionals and smooth points in Orlicz function spaces equipped with the Orlicz norm, Math. Jap. 39(2) (1994) 271–280.Google Scholar
  6. M. Cieielski, A. Kamińska, R. Płuciennik: Gâteaux derivatives and their applications to approximation in Lorentz spaces Γp,w, Math. Nachr. 282(9) (2009) 1242–1264.https://doi.org/10.1002/mana.200810798Google Scholar
  7. M. M. Day: Normed Linear Spaces, Springer, Berlin (1962).https://doi.org/10.1007/978-3-662-41637-2Google Scholar
  8. R. Deville, G. Godefroy, V. Zizler: Smoothness and Renormings in Banach Spaces, Pitman Monographs and Surveys in Pure and Applied Mathematics 64, Longman Scientific & Technical, Harlow (1993).Google Scholar
  9. A. Kamińska, H. J. Lee: M -ideal properties in Marcinkiewicz spaces, Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 2004, Spec. Iss. (2004) 123–144.Google Scholar
  10. A. Kamińska, H. J. Lee, G. Lewicki: Extreme and smooth points in Lorentz and Marcinkiewicz spaces with applications to contractive projections, Rocky Mt. J. Math. 39(5) (2009) 1533–1572.https://doi.org/10.1216/RMJ-2009-39-5-1533Google Scholar
  11. L. V. Kantorovich, G. P. Akilov: Functional Analysis, 2nd Ed., Pergamon Press, Oxford (1982).Google Scholar
  12. S. G. Kreĭn, Yu. Ī. Petunīn and E. M. Semënov: Interpolation of Linear Operators, Translations of Mathematical Monographs 54, AMS, Providence (1982).Google Scholar
  13. F. E. Levis, H. H. Cuenya: Gâteaux differentiability in Orlicz-Lorentz spaces and applications, Math. Nachr. 280(11) (2007) 1282–1296.https://doi.org/10.1002/mana.200410553Google Scholar
  14. J. Lindenstrauss, L. Tzafriri: Classical Banach Spaces II, Springer, Berlin (1979).https://doi.org/10.1007/978-3-662-35347-9Google Scholar
  15. I. Singer: The Theory of Best Approximation and Functional Analysis, CBMS-NSF Regional Conference Series in Applied Mathematics 13, SIAM, Philadelphia (1974).https://doi.org/10.1137/1.9781611970548Google Scholar

A. Kamińska, A. M. Parrish. “Smooth Points in Marcinkiewicz Function Spaces.” Journal of Convex Analysis 18 (2011), No. 2, 379–390. https://doi.org/10.68381/jca18021