Multiple Hilbert transforms associated with polynomials
About this Title
Joonil Kim
Publication: Memoirs of the American Mathematical Society
Publication Year:
2015; Volume 237, Number 1119
ISBNs: 978-1-4704-1435-1 (print); 978-1-4704-2505-0 (online)
DOI: http://dx.doi.org/10.1090/memo/1119
Published electronically: January 21, 2015
Keywords:Multiple Hilbert transform, Newton polyhedron, face, cone
Table of Contents
Chapters
- Chapter 1. Introduction
- Chapter 2. Definitions of Polyhedra, Their Faces and Cones
- Chapter 3. Main Theorem and Background
- Chapter 4. Combinatorial Lemmas
- Chapter 5. Descending Faces vs. Ascending Cones
- Chapter 6. Preliminary Results of Analysis
- Chapter 7. Proof of Sufficiency
- Chapter 8. Necessity Theorem
- Chapter 9. Preliminary Lemmas for Necessity Proof
- Chapter 10. Proof of Necessity
- Chapter 11. Proofs of Corollary 3.1 and Main Theorem 3.1
- Chapter 12. Appendix
Abstract
Let with , and set the family of all vector polynomials, Given , we consider a class of multi-parameter oscillatory singular integrals, When , the integral for any is bounded uniformly in and . However, when , the uniform boundedness depends on each individual polynomial . In this paper, we fix and find a necessary and sufficient condition on that
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