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An application of weighted Hardy spaces to the Navier-Stokes equations. (English) Zbl 1306.46040
Summary: In this article, we consider the mapping properties of convolution operators with smooth functions on weighted Hardy spaces $$H^p(w)$$ with $$w$$ belonging to Muckenhoupt class $$A_\infty$$. As a corollary, one obtains decay estimates for the heat semigroup on weighted Hardy spaces. After a weighted version of the div-curl lemma is established, these estimates on weighted Hardy spaces are applied to the investigation of the decay property of global mild solutions to Navier-Stokes equations with the initial data belonging to weighted Hardy spaces.

##### MSC:
 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 42B30 $$H^p$$-spaces 42B35 Function spaces arising in harmonic analysis 35Q30 Navier-Stokes equations
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