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Discovery Projects - Grant ID: DP130101302

Title
Discovery Projects - Grant ID: DP130101302
Funding
ARC | Discovery Projects
Contract (GA) number
DP130101302
Start Date
2013/01/01
End Date
2015/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/DP130101302

 

  • The limitations of the Poincar{\'e} inequality

    We examine the validity of the Poincar\'e inequality for degenerate, second-order, elliptic operators $H$ in divergence form on $L_2(\Ri^{n}\times\Ri^{m})$. We assume the coefficients are real symmetric and $a_1H_\delta\geq H\geq a_2H_\delta$ for some $a_1,a_2>0$ where $H_\delta$ is a generalized Gru\v{s}in operator, \[ H_\delta=-\nabla_{x_1}\,|x_1|^{(2\delta_1,2\delta_1')}\,\nabla_{x_1}-|x_1|^{(2\delta_2,2\delta_2')}\,\nabla_{x_2}^2 \;. \] Here $x_1\in\Ri^n$, $x_2\in\Ri^m$, $\delta_1,\delta_...

    Hardy spaces on metric measure spaces with generalized sub-gaussian heat kernel estimates

    Accepted for publication; International audience; Hardy space theory has been studied on manifolds or metric measure spaces equipped with either Gaussian or sub-Gaussian heat kernel behaviour. However, there are natural examples where one finds a mix of both behaviour (locally Gaussian and at infinity sub-Gaussian) in which case the previous theory doesn't apply. Still we define molecular and square function Hardy spaces using appropriate scaling, and we show that they agree with Lebesgue spa...
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