Endpoint multiplier theorems of Marcinkiewicz type
Terence Tao, Jim Wright
Abstract
We establish sharp (H1, L1,q) and local (L r L, L1,q) mapping properties for rough one-dimensional multipliers. In particular, we show that the multipliers in the Marcinkiewicz multiplier theorem map H1 to L1,∞ and L 1/2 L to L1,∞, and that these estimates are sharp.
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