Search results for "B3"
showing 10 items of 193 documents
The method of moving planes: a quantitative approach
2018
We review classical results where the method of the moving planes has been used to prove symmetry properties for overdetermined PDE's boundary value problems (such as Serrin's overdetermined problem) and for rigidity problems in geometric analysis (like Alexandrov soap bubble Theorem), and we give an overview of some recent results related to quantitative studies of the method of moving planes, where quantitative approximate symmetry results are obtained.
Characterizing boundedness of metaplectic Toeplitz operators
2023
We study Toeplitz operators on the Bargmann space, with Toeplitz symbols given by exponentials of complex quadratic forms. We show that the boundedness of the corresponding Weyl symbols is necessary for the boundedness of the operators, thereby completing the proof of the Berger-Coburn conjecture in this case. We also show that the compactness of such Toeplitz operators is equivalent to the vanishing of their Weyl symbols at infinity.
Radial Maximal Function Characterizations of Hardy Spaces on RD-Spaces and Their Applications
2009
Let ${\mathcal X}$ be an RD-space with $\mu({\mathcal X})=\infty$, which means that ${\mathcal X}$ is a space of homogeneous type in the sense of Coifman and Weiss and its measure has the reverse doubling property. In this paper, we characterize the atomic Hardy spaces $H^p_{\rm at}(\{\mathcal X})$ of Coifman and Weiss for $p\in(n/(n+1),1]$ via the radial maximal function, where $n$ is the "dimension" of ${\mathcal X}$, and the range of index $p$ is the best possible. This completely answers the question proposed by Ronald R. Coifman and Guido Weiss in 1977 in this setting, and improves on a deep result of Uchiyama in 1980 on an Ahlfors 1-regular space and a recent result of Loukas Grafakos…
New Orlicz-Hardy Spaces Associated with Divergence Form Elliptic Operators
2009
Let $L$ be the divergence form elliptic operator with complex bounded measurable coefficients, $\omega$ the positive concave function on $(0,\infty)$ of strictly critical lower type $p_\oz\in (0, 1]$ and $\rho(t)={t^{-1}}/\omega^{-1}(t^{-1})$ for $t\in (0,\infty).$ In this paper, the authors study the Orlicz-Hardy space $H_{\omega,L}({\mathbb R}^n)$ and its dual space $\mathrm{BMO}_{\rho,L^\ast}({\mathbb R}^n)$, where $L^\ast$ denotes the adjoint operator of $L$ in $L^2({\mathbb R}^n)$. Several characterizations of $H_{\omega,L}({\mathbb R}^n)$, including the molecular characterization, the Lusin-area function characterization and the maximal function characterization, are established. The …
Weyl symbols and boundedness of Toeplitz operators
2019
International audience; We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of inhomogeneous quadratic polynomials. It is shown that the boundedness of such operators is implied by the boundedness of the corresponding Weyl symbols.
Bounded compositions on scaling invariant Besov spaces
2012
For $0 < s < 1 < q < \infty$, we characterize the homeomorphisms $��: \real^n \to \real^n$ for which the composition operator $f \mapsto f \circ ��$ is bounded on the homogeneous, scaling invariant Besov space $\dot{B}^s_{n/s,q}(\real^n)$, where the emphasis is on the case $q\not=n/s$, left open in the previous literature. We also establish an analogous result for Besov-type function spaces on a wide class of metric measure spaces as well, and make some new remarks considering the scaling invariant Triebel-Lizorkin spaces $\dot{F}^s_{n/s,q}(\real^n)$ with $0 < s < 1$ and $0 < q \leq \infty$.
Existence results for parametric boundary value problems involving the mean curvature operator
2014
In this note we propose a variational approach to a parametric differential problem where a prescribed mean curvature equation is considered. In particular, without asymptotic assumptions at zero and at infinity on the potential, we obtain an explicit positive interval of parameters for which the problem under examination has at least one nontrivial and nonnegative solution.
Zooplankton biodiversity and community structure vary along spatiotemporal environmental gradients in restored peridunal ponds
2015
<p>Zooplankton assemblages in neighboring ponds can show important spatial and temporal heterogeneity. Disentangling the influence of regional versus local factors, and of deterministic versus stochastic processes has been recently highlighted in the context of the metacommunity theory. In this study, we determined patterns of temporal and spatial variation in zooplankton diversity along one hydrological year in restored ponds of different hydroperiod and age. The following hypotheses regarding the assembling of species over time were tested: i) dispersal is not limited in our study system due to its small area and high exposure to dispersal vectors; ii) community dissimilarity among …
The Hammerhead Ribozyme: A Long History for a Short RNA
2017
Small nucleolytic ribozymes are a family of naturally occurring RNA motifs that catalyse a self-transesterification reaction in a highly sequence-specific manner. The hammerhead ribozyme was the first reported and the most extensively studied member of this family. However, and despite intense biochemical and structural research for three decades since its discovery, the history of this model ribozyme seems to be far from finished. The hammerhead ribozyme has been regarded as a biological oddity typical of small circular RNA pathogens of plants. More recently, numerous and new variations of this ribozyme have been found to inhabit the genomes of organisms from all life kingdoms, although th…
Solution Structure of the R3H Domain from Human Sμbp-2
2003
The R3H domain is a conserved sequence motif, identified in over 100 proteins, that is thought to be involved in polynucleotide-binding, including DNA, RNA and single-stranded DNA. In this work the 3D structure of the R3H domain from human Smubp-2 was determined by NMR spectroscopy. It is the first 3D structure determination of an R3H domain. The fold presents a small motif, consisting of a three-stranded antiparallel beta-sheet and two alpha-helices, which is related to the structures of the YhhP protein and the C-terminal domain of the translational initiation factor IF3. The similarities are non-trivial, as the amino acid identities are below 10%. Three conserved basic residues cluster o…