In this chapter, we consider associate spaces LΦ1 of Orlicz spaces LΦ. Using the Legendre transform of an Orlicz function Φ, we define the conjugate Orlicz function ψ just as the Legendre transform of Φ. We prove that the spaces LΦ1 and Lψ coincide as sets and ∥·∥Lψ ≤ ∥·∥LΦ1 ≤ 2∥ ∥Lψ. The duality between LΦ and Lψ is studied in detail.
|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)