The Commutant of the Laplace Operator in Lp(R)

✍ Scribed by Werner J. Ricker

• Publisher: John Wiley and Sons
• Year: 1990
• Tongue: English
• Weight: 477 KB
• Volume: 146
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19901460302

✦ Synopsis

Abstract

Let L = ‐ d^2^/dx^2^ be the Laplace operator in L^p^(R), 1<p < ∞. It is shown that a bounded operator T in L^p^(R) commutes with L, in the sense that the domain D of L is T‐invariant and TLf = LTf for each f in D, if and only if T commutes with all (bounded) multiplier operators corresponding to symmetric p‐multipliers on R. The bicommutant L consists of all the symmetric p‐multiplier operators.