Related papers: Riesz transforms in one dimension

We consider a class of non-doubling manifolds $\mathcal{M}$ defined by taking connected sum of finite Riemannian manifolds with dimension N which has the form $\mathbb{R}^{n_i}\times \mathcal{M}_i$ and the Euclidean dimension $n_i$ are not…

In the setting of Euclidean space with the Gaussian measure g, we consider all first-order Riesz transforms associated to the infinitesimal generator of the Ornstein-Uhlenbeck semigroup. These operators are known to be bounded on L^p(g),…

We study $L^p$ bounds for two kinds of Riesz transforms on $\mathbb{R}^d$ related to the harmonic oscillator. We pursue an explicit estimate of their $L^p$ norms that is independent of the dimension $d$ and linear in $\max(p, p/(p-1))$.

We study equilibrium measures for Riesz gases in dimension $d$ with pairwise interaction kernel $|x-y|^{-s}$, subject to radially symmetric external fields. We characterise broad classes of confining potentials for which the equilibrium…

One considers the class of complete non-compact Riemannian manifolds whose heat kernel satisfies Gaussian estimates from above and below. One shows that the Riesz transform is $L^p$ bounded on such a manifold, for $p$ ranging in an open…

We prove the boundedness on $L^p$, $1<p<\infty$, of operators on manifolds which arise by taking conditional expectation of transformations of stochastic integrals. These operators include various classical operators such as second order…

Let $L$ be a one to one operator of type $\omega$ having a bounded $H_\infty$ functional calculus and satisfying the $k$-Davies-Gaffney estimates with $k\in{\mathbb N}$. In this paper, the authors introduce the Hardy space…

We present a new proof of the dimensionless $L^p$ boundedness of the Riesz vector on manifolds with bounded geometry. Our proof has the significant advantage that it allows for a much stronger conclusion, namely that of a new dimensionless…

Given a sequence of complete Riemannian manifolds $(M_n)$ of the same dimension, we construct a complete Riemannian manifold $M$ such that for all $p \in (1,\infty)$ the $L^p$-norm of the Riesz transform on $M$ dominates the $L^p$-norm of…

We study differentiability properties of Riesz potentials of finite Borel measures in dimension d larger than 2. The Riesz kernel has homogeneity 2-d. In dimension 2 we consider logarithmic potentials. We introduce a notion of…

We show that the $L^p$ boundedness, $p>2$, of the Riesz transform on a complete non-compact Riemannian manifold with upper and lower Gaussian heat kernel estimates is equivalent to a certain form of Sobolev inequality. We also characterize…

We show that the norm of the vector of Riesz transforms as operator in the weighted Lebesgue space L^2(w) is bounded by a constant multiple of the first power of the Poisson-A_2 characteristic of w. The bound is free of dimension. Our…

Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a variable exponent function satisfying that there exists a constant $p_0\in(0,p_-)$, where $p_-:=\mathop{\mathrm {ess\,inf}}_{x\in \mathbb R^n}p(x)$, such that the Hardy-Littlewood maximal…

We consider a class of manifolds $\mathcal{M}$ obtained by taking the connected sum of a finite number of $N$-dimensional Riemannian manifolds of the form $(\mathbb{R}^{n_i}, \delta) \times (\mathcal{M}_i, g)$, where $\mathcal{M}_i$ is a…

Let $G = N \rtimes A$, where $N$ is a stratified group and $A = \mathbb{R}$ acts on $N$ via automorphic dilations. Homogeneous sub-Laplacians on $N$ and $A$ can be lifted to left-invariant operators on $G$ and their sum is a sub-Laplacian…

In this paper, we prove that the $L^p(\mathbb{R}^d)$ norm of the maximal truncated Riesz transform in terms of the $L^p(\mathbb{R}^d)$ norm of Riesz transform is dimension-free for any $2\leq p<\infty$, using integration by parts formula…

We study the $L^{2}$-boundedness of the $3$-dimensional (Heisenberg) Riesz transform on intrinsic Lipschitz graphs in the first Heisenberg group $\mathbb{H}$. Inspired by the notion of vertical perimeter, recently defined and studied by…

We prove a T1 theorem for fractional vector Riesz transforms mapping one weighted Sobolev space to another, where the weights are doubling measures on Euclidean space. Boundedness is characterized by the classical A_2 condition and two dual…

In this paper we consider $L^p$ boundedness of some commutators of Riesz transforms associated to Schr\"{o}dinger operator $P=-\Delta+V(x)$ on $\mathbb{R}^n, n\geq 3$. We assume that $V(x)$ is non-zero, nonnegative, and belongs to $B_q$ for…

We give a simple proof of L^p boundedness of iterated commutators of Riesz transforms and a product BMO function. We use a representation of the Riesz transforms by means of simple dyadic operators - dyadic shifts - which in turn reduces…