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February 2011 Riesz transforms on generalized Hardy spaces and a uniqueness theorem for the Navier-Stokes equations
Eiichi NAKAI, Tsuyoshi YONEDA
Hokkaido Math. J. 40(1): 67-88 (February 2011). DOI: 10.14492/hokmj/1300108399

Abstract

The purpose of this paper is twofold. Let Rj (j = 1,2, ... , n) be Riesz transforms on $\mathbb{R}$n. First we prove the convergence of truncated operators of RiRj in generalized Hardy spaces. Our first result is an extension of the convergence in Lp($\mathbb{R}$^n) (1 < p < ∞). Secondly, as an application of the first result, we show a uniqueness theorem for the Navier-Stokes equation. J. Kato (2003) established the uniqueness of solutions of the Navier-Stokes equations in the whole space when the velocity field is bounded and the pressure field is a BMO-valued locally integrable-in-time function for bounded initial data. We extend the part "BMO-valued" in his result to "generalized Campanato space valued". The generalized Campanato spaces include L1, BMO and homogeneous Lipschitz spaces of order α (0 < α < 1).

Citation

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Eiichi NAKAI. Tsuyoshi YONEDA. "Riesz transforms on generalized Hardy spaces and a uniqueness theorem for the Navier-Stokes equations." Hokkaido Math. J. 40 (1) 67 - 88, February 2011. https://doi.org/10.14492/hokmj/1300108399

Information

Published: February 2011
First available in Project Euclid: 14 March 2011

zbMATH: 1221.35283
MathSciNet: MR2790830
Digital Object Identifier: 10.14492/hokmj/1300108399

Subjects:
Primary: 35Q30, 76D05
Secondary: 42B30, 42B35

Rights: Copyright © 2011 Hokkaido University, Department of Mathematics

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Vol.40 • No. 1 • February 2011
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