Revista Matemática Iberoamericana

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Volume 17, Issue 3, 2001, pp. 521–558
DOI: 10.4171/RMI/303

Published online: 2001-12-31

Endpoint multiplier theorems of Marcinkiewicz type

Terence Tao[1] and James Wright[2]

(1) University of California Los Angeles, United States
(2) University of Edinburgh, UK

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.

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Tao Terence, Wright James: Endpoint multiplier theorems of Marcinkiewicz type. Rev. Mat. Iberoam. 17 (2001), 521-558. doi: 10.4171/RMI/303