Estimates for rough Fourier integral and pseudodifferential operators and applications to the boundedness of multilinear operators

Abstract

We study the boundedness of rough Fourier integral and pseudodifferential operators, defined by general rough Hörmander class amplitudes, on Banach and quasi-Banach $L^p$ spaces. Thereafter we apply the aforementioned boundedness in order to improve on some of the existing boundedness results for Hörmander class bilinear pseudodifferential operators and certain classes of bilinear (as well as multilinear) Fourier integral operators. For these classes of amplitudes, the boundedness of the aforementioned Fourier integral operators turn out to be sharp. Furthermore we also obtain results for rough multilinear operators.

arXiv admin note: substantial text overlap with arXiv:1111.4652 Various typos have been eliminated

References in corpus (2)

• Global and local regularity of Fourier integral operators on weighted and unweighted spaces
• Multilinear pseudodifferential operators beyond Calderón-Zygmund theory

Cited by in corpus (7)

• Local and global estimates for hyperbolic equations in Besov-Lipschitz and Triebel-Lizorkin spaces
• Regularity of Fourier integral operators with amplitudes in general Hörmander classes
• Global regularity properties for a class of Fourier integral operators
• A local-to-global boundedness argument and Fourier integral operators
• A local-to-global weak (1,1) type argument and applications to Fourier integral operators
• Some endpoint estimates for bilinear paraproducts and applications
• Transference of local to global $L^2$ maximal estimates for dispersive partial differential equations