Endpoint multiplier theorems of Marcinkiewicz type

Abstract

We establish sharp (H^1, L^{1,q}) and local ( L log ^r L, L^{1,q} ) mapping properties for rough one-dimensional multipliers. In particular we show that the multipliers in the Marcinkiewicz multiplier theorem map H^1 to L^{1,\infty} and L log ^{1/2}L to L^{1,\infty} , and that these estimates are sharp.

Locations

• Revista Matemática Iberoamericana - View - PDF
• arXiv (Cornell University) - PDF
• arXiv (Cornell University) - View
• Revista Matemática Iberoamericana - View - PDF
• arXiv (Cornell University) - PDF
• arXiv (Cornell University) - View