1,138
Views
1
CrossRef citations to date
0
Altmetric
Notes

Simple Proofs of the Uniform Convexity of Lp and the Riesz Representation Theorem for Lp

References

  • Adams, R. A., Fournier, J. J. F. (2003). Sobolev Spaces, 2nd ed. Pure and Applied Mathematics, Vol.140. Amsterdam: Elsevier.
  • Clarkson, J. A. (1936). Uniformly convex spaces. Trans. Amer. Math. Soc. 40(3): 396–414.
  • Folland, G. B. (1999). Real analysis, Modern Techniques and Their Applications, 2nd ed. Pure and Applied Mathematics. New York: John Wiley & Sons.
  • Friedrichs, K. O. (1970). On Clarkson’s inequalities. Comm. Pure Appl. Math. 23(4): 603–607.
  • Hanche-Olsen, H. (2006). On the uniform convexity of Lp. Proc. Amer. Math. Soc. 134(8): 2359–2362.
  • Hanner, O. (1956). On the uniform convexity of Lp and lp. Ark. Mat. 3(3): 239–244.
  • Komornik, V. (2016). Lectures on Functional Analysis and the Lebesgue Integral. London: Springer-Verlag.
  • Maligranda, L., Persson, L. E. (1992). On Clarkson’s inequalities and interpolation. Math. Nachr. 155(1): 187–197.
  • McShane, E. J. (1950). Linear functionals on certain Banach spaces, Proc. Amer. Math. Soc. 1(3): 402–408.
  • Meir, A. (1984). On the uniform convexity of spaces, . Illinois J. Math. 28(3): 420–424.
  • Ramaswamy, S. (1978). A simple proof of Clarkson’s inequality. Proc. Amer. Math. Soc. 68(2): 249–250.
  • Ringrose, J. R. (1959). A note on uniformly convex spaces. J. London Math. Soc. 34(1): 92.
  • Roselli, P., Willem, M. (2002). A convexity inequality, Amer. Math. Monthly. 109(1): 64–70.
  • Rudin, W. (1987). Real and Complex Analysis, 3rd ed. New York: McGraw-Hill.
  • Schwartz, J. (1951). A note on the space , Proc. Amer. Math. Soc. 2(2): 270–275.
  • Simmons, G. F. (1963). Introduction to Topology and Modern Analysis. New York: McGraw-Hill.
  • Takáč, P. (2010). Variational methods and linearization tools towards the spectral analysis of the p-Laplacian, especially for the Fredholm alternative. Proceedings of the 2007 Conference on Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems. Electron. J. Differ. Equ. Conf. 18: 67–105.
  • Willem, M. (2013). Functional analysis, Fundamentals and Applications. New York: Birkhäuser.
  • Zălinescu, C. (1983). On uniformly convex functions. J. Math. Anal. Appl. 95(2): 344–374.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.