A multiplier theorem using the Schechter's method of interpolation

✍ Scribed by Marı́a J. Carro

• Book ID: 104142792
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 173 KB
• Volume: 120
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1016/s0021-9045(02)00036-9

✦ Synopsis

Let m be a measurable bounded function and let us assume that there exists a bounded functions S so that mðxÞSðxÞ itÀ1 is a Fourier multiplier on L p uniformly in tAR: Then, using the analytic interpolation theorem of Stein, one can show that necessarily m is a L p multiplier. The purpose of this work is to show that under the above conditions, it holds that, for every kAN; mðlog SÞ k AM p : The technique is based on the Schechter's interpolation method.