Laurent Moonens - LM-Orsay

Laurent Moonens
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Laurent Moonens

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Mathematics - Classical Analysis and ODEs (3)
Mathematics - Analysis of PDEs (2)
Mathematics - Functional Analysis (1)

Publications Authored By Laurent Moonens

In this paper, we characterize all the distributions $F \in \mathcal{D}'(U)$ such that there exists a continuous weak solution $v \in C(U,\mathbb{C}^{n})$ (with $U \subset \Omega$) to the divergence-type equation $$L_{1}^{*}v_{1}+... Read More

We show that, given some lacunary sequence of angles $\mathbf{\theta}=(\theta_j)_{j\in\N}$ not converging too fast to zero, it is possible to build a rare differentiation basis $\mathcal{B}$ of rectangles parallel to the axes that differentiates $L^1(\mathbb{R}^2)$ while the basis $\mathcal{B}_{\mathbf{\theta}}$ obtained from $\mathcal{B}$ by allowing its elements to rotate around their lower left vertex by the angles $\theta_j$, $j\in\mathbb{N}$, fails to differentiate all Orlicz spaces lying between $L^1(\mathbb{R}^2)$ and $L\log L(\mathbb{R}^2)$. Read More

In this work we investigate families of translation invariant differentiation bases $B$ of rectangles in $R^n$, for which $L\log^{n-1}L(R^n)$ is the largest Orlicz space that $B$ differentiates. In particular, we improve on techniques developed by A.~Stokolos 1988 and 2008. Read More

Let $w\in L^1\_{loc}(\R^n)$ be apositive weight. Assuming that a doubling condition and an $L^1$ Poincar\'e inequality on balls for the measure $w(x)dx$, as well as a growth condition on $w$, we prove that the compact subsets of $\R^n$ which are removable for the distributional divergence in $L^{\infty}\_{1/w}$ are exactly those with vanishing weighted Hausdorff measure. We also give such a characterization for $L^p\_{1/w}$, $1\textless{}p\textless{}+\infty$, in terms of capacity. Read More