Endpoint multiplier theorems of Marcinkiewicz type

Details Endpoint multiplier theorems of Marcinkiewicz type Endpoint multiplier theorems of Marcinkiewicz type

2000-01-09

arxiv.org/abs/math/0001050v1

Mathematics

Classical Analysis and ODEs

28 pages, no figures, submitted to Revista Mat. Iber

Scientific paper

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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