Hardy spaces and oscillatory singular integrals. II

Yibiao Pan

Vol. 168 (1995), No. 1, 167–182

DOI: 10.2140/pjm.1995.168.167

Abstract

We consider oscillatory singular integral operators with real-analytic phases. The uniform boundedness from H_E¹ → L¹ of such operators is proved, where H_E¹ is a variant of the standard Hardy space H¹. The result is false for general C^∞ phases. This work is a continuation of earlier work by Phong and Stein (on bilinear phases) and the author (on polynomial phases).

Mathematical Subject Classification 2000

Primary: 42B20

Secondary: 47G10

Milestones

Received: 6 October 1992

Revised: 1 September 1993

Published: 1 March 1995