Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Geometry of Lebesgue-Bochner function spaces—smoothness
HTML articles powered by AMS MathViewer

by I. E. Leonard and K. Sundaresan
Trans. Amer. Math. Soc. 198 (1974), 229-251
DOI: https://doi.org/10.1090/S0002-9947-1974-0367652-5

Abstract:

There exist real Banach spaces $E$ such that the norm in $E$ is of class ${C^\infty }$ away from zero; however, for any $p,1 \leqslant p \leqslant \infty$, the norm in the Lebesgue-Bochner function space ${L_p}(E,\mu )$ is not even twice differentiable away from zero. The main objective of this paper is to give a complete determination of the order of differentiability of the norm function in this class of Banach spaces.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 46E40, 58C20
  • Retrieve articles in all journals with MSC: 46E40, 58C20
Bibliographic Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 198 (1974), 229-251
  • MSC: Primary 46E40; Secondary 58C20
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0367652-5
  • MathSciNet review: 0367652