The weak (1,1) boundedness of Fourier integral operators with complex phases

2024/02/14 by Cardona, Duván, Ruzhansky, Michael
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2402.09054

Abstract

Let T be a Fourier integral operator of order -(n-1)/2 associated with a canonical relation locally parametrised by a real-phase function. A fundamental result due to Seeger, Sogge, and Stein proved in the 90's, gives the boundedness of T from the Hardy space H¹ into L¹. Additionally, it was shown by T. Tao the weak (1,1) type of T. In this work, we establish the weak (1,1) boundedness of a Fourier integral operator T of order -(n-1)/2 when it has associated a canonical relation parametrised by a complex phase function. This result in the complex-valued setting, cannot be derived from its counterpart in the real-valued case.

Related

• The weak-type (1,1) of Fourier integral operators of order -(n-1)/2
• Global L2-Boundedness Theorems for Semiclassical Fourier Integral Operators with Complex Phase
• A class of multi-parameter Fourier integral operators: endpoint Hardy space bounds
• Sharpness of Seeger-Sogge-Stein orders for the weak (1,1) boundedness of Fourier integral operators
• L^p-boundedness of multi-parameter Fourier integral operators