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Endpoint multiplier theorems of Marcinkiewicz type

Terence Tao·Jim Wright
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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.

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Terence Tao, Jim Wright. 2000-01-09. Endpoint multiplier theorems of Marcinkiewicz type. https://arxiv.org/abs/math/0001050

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