Related papers: L^p-summability of Riesz means for the sublaplacia…

In this article we show that the $\Z_p[\zeta_{p^f-1}]$-order $\Z_p[\zeta_{p^f-1}]\SL_2(p^f)$ can be recognized among those orders whose reduction modulo $p$ is isomorphic to $\F_{p^f}\SL_2(p^f)$ using only ring-theoretic properties (in…

Let $M$ be a complete non-compact Riemannian manifold satisfying the doubling volume property. Let $\overrightarrow{\Delta}$ be the Hodge-de Rham Laplacian acting on 1-differential forms. According to the Bochner formula,…

We prove a superposition principle for Riesz potentials of nonnegative continuous functions on Lie groups of Heisenberg type. More precisely, we show that the Riesz potential $$ R_\alpha(\rho)(g) = \int_{\G} N(g^{-1} g')^{\alpha-Q} \rho(g')…

We consider the Schatten spaces S^p in the framework of operator space theory and for any $1\leq p\not=2<\infty$, we characterize the completely 1-complemented subspaces of S^p. They turn out to be the direct sums of spaces of the form…

Lipschitz decomposition is a useful tool in the design of efficient algorithms involving metric spaces. While many bounds are known for different families of finite metrics, the optimal parameters for $n$-point subsets of $\ell_p$, for $p >…

In this note, we extend the well-known theorems of M. Riesz and Zygmund on conjugate functions as follows. Let $\Omega$ be a domain in $\mathbb C^n$. Suppose that $f=u+iv\in \mathcal O(\Omega)$ satisfies $v(z_0)=0$ for some $z_0\in \Omega$.…

In this paper, we show the equivalence between the boundedness of the Riesz transform $d\Delta^{-1/2}$ on $L^p$, $p\in (2,p_0)$, and the equality $H^p=L^p$, $p\in(2,p_0)$, in the class of manifold whose measure is doubling and for which the…

Let $\M$ be a smooth connected non-compact manifold endowed with a smooth measure $\mu$ and a smooth locally subelliptic diffusion operator $L$ satisfying $L1=0$, and which is symmetric with respect to $\mu$. We show that if $L$ satisfies,…

We consider Bochner-Riesz means on weighted $L^p$ spaces, at the critical index $\lambda(p)=d(\frac 1p-\frac 12)-\frac 12$. For every $A_1$-weight we obtain an extension of Vargas' weak type $(1,1)$ inequality in some range of $p>1$. To…

We characterise functions for the dual spaces of entire functions f such that fe^{-\phi}\in L^p(\C^n,\rho^{-2}dA), 0<p\leq 1, where \phi is a subharmonic weight and \rho^{-2} is a positive function called under certain conditions…

The symplectic Stiefel manifold, denoted by $\mathrm{Sp}(2p,2n)$, is the set of linear symplectic maps between the standard symplectic spaces $\mathbb{R}^{2p}$ and $\mathbb{R}^{2n}$. When $p=n$, it reduces to the well-known set of $2n\times…

We study the validity of the $L^p$ inequality for the Riesz transform when $p>2$ and of its reverse inequality when $p<2$ on complete Riemannian manifolds under the doubling property and some Poincar\'e inequalities.

The $p$-Laplacian operator $\Delta_pu={\rm div }\left(|\nabla u|^{p-2}\nabla u\right)$ is not uniformly elliptic for any $p\in(1,2)\cup(2,\infty)$ and degenerates even more when $p\to \infty$ or $p\to 1$. In those two cases the Dirichlet…

We establish various $L^{p}$ estimates for the Schr\"odinger operator $-\Delta+V$ on Riemannian manifolds satisfying the doubling property and a Poincar\'e inequality, where $\Delta $ is the Laplace-Beltrami operator and $V$ belongs to a…

Let $v \ne 0$ be a vector in $\R^n$. Consider the Laplacian on $\R^n$ with drift $\Delta_{v} = \Delta + 2v\cdot \nabla$ and the measure $d\mu(x) = e^{2 \langle v, x \rangle} dx$, with respect to which $\Delta_{v}$ is self-adjoint. This…

We show a Gromov-Hausdorff approximation to the product of the standard spheres $S^{n-p}\times S^p$ for Riemannian manifolds with positive Ricci curvature under some pinching condition on the eigenvalues of the Laplacian acting on functions…

We prove some isoperimetric type inequalities for real harmonic functions in the unit disk belonging to the Hardy space $h^p$, $p>1$ and for complex harmonic functions in $h^4$. The results extend some recent results on the area. Further we…

Let $X$ be a convex co-compact hyperbolic surface and let $\delta$ be the Hausdorff dimension of the limit set of the underlying discrete group. We show that the density of the resonances of the Laplacian in strips ${\sigma\leq \re(s) \leq…

We develop a new approach to the invertibility of the layer potentials on $L^p$ associated with elliptic equations and systems in Lipschitz domains. As a consequence, for $n\ge 4$ and $(2(n-1)/(n+1))-\epsilon<p<2$, we obtain the solvability…

We study several problems related to the $\ell^p$ boundedness of Riesz transforms for graphs endowed with so-called bounded Laplacians. Introducing a proper notion of gradient of functions on edges, we prove for $p\in(1,2]$ an $\ell^p$…