In this chapter we study the class of Lp spaces, 1 ≤ p≤∞, which is one of the most important classes of symmetric spaces. We begin with the Hölder and Minkowski inequalities and prove that Lp is a symmetric space for all 1 ≤ p ≤ ∞. In the case 1 ≤ p < ∞, we show that Lp is separable and describe its dual.
|Title of host publication||Developments in Mathematics|
|Publisher||Springer New York LLC|
|Number of pages||11|
|State||Published - 1 Jan 2016|
|Name||Developments in Mathematics|
ASJC Scopus subject areas
- Mathematics (all)