Related papers: The Riesz transform for the harmonic oscillator in…
We consider integrals of spherical harmonics with Fourier exponents on the sphere $S^n ,\, n \geq 1$. Such transforms arise in the framework of the theory of weighted Radon transforms and vector diffraction in electromagnetic fields theory.…
In this short article we obtain the non-asymptotic upper and low estimations for linear and bilinear weight Riesz's functional through the Lebesgue spaces.
We develop a theory of extrapolation for weights that satisfy a generalized reverse H\"older inequality in the scale of Orlicz spaces. This extends previous results by Auscher and Martell [2] on limited range extrapolation. As an…
In this paper we obtain some Strichartz estimates for the Schr\"odinger equation associated to the harmonic oscillator and the Laplacian. Our main tool will be some embeddings between Lebesgue spaces and suitable Triebel-Lizorkin spaces.
In this note, we study both the Riesz and reverse Riesz transforms on broken line. This model can be described by $(-\infty, -1] \cup [1,\infty)$ equipped with the measure $d\mu = |r|^{d_{1}-1}dr$ for $r \le -1$ and $d\mu = r^{d_{2}-1}dr$…
In a previous paper by one of us, a "compact version" of Rubio de Francia's weighted extrapolation theorem was proved, which allows one to extrapolate the compactness of an operator from just one space to the full range of weighted spaces,…
In this article, we establish an analogue of Pitt's inequality for the Strichartz Fourier transform on the Heisenberg group $\mathbb{H}^n$. By exploiting the scalar-valued formulation of the transform and the framework of decreasing…
We review the relation between compact asymptotic spectral measures and certain positive asymptotic morphism on locally compact spaces via asymptotic Riesz representation theorem, as introduced by Martinez and Trout [3]. Applications to…
This article focuses on $L^p$ estimates for objects associated to elliptic operators in divergence form: its semigroup, the gradient of the semigroup, functional calculus, square functions and Riesz transforms. We introduce four critical…
We prove the Plancherel formula for spherical Schwartz functions on a reductive symmetric space. Our starting point is an inversion formula for spherical smooth compactly supported functions. The latter formula was earlier obtained from the…
In this note we prove various sharp boundedness results on suitable Hardy type spaces for Riesz transforms of arbitrary order on noncompact symmetric spaces of arbitrary rank.
The paper is devoted to the investigation of Esscher's transform on high dimensional Euclidean spaces in the light of its application to the central limit theorem. With this tool, we explore necessary and sufficient conditions of normal…
We prove sharp version of Riesz-Fej\'er inequality for functions in harmonic Hardy space $h^p(\mathbb{D})$ on the unit disk $\mathbb{D}$, for $p>1,$ thus extending the result from \cite{KPK} and resolving the posed conjecture.
In this paper, we prove analogues of O'Neil's inequalities for the convolution in the weighted Lebesgue spaces. We also establish the weighted two-sided norm inequalities for the potential operator.
We obtain inequalities for the Riesz means for the discrete spectrum of a class of self-adjoint compact integral operators. Such bounds imply some inequalities for the counting function of the Dirichlet boundary problem for the Laplace…
In this work we obtain weighted $L^p$, $1<p<\infty$, and weak $L\log L$ estimates for the commutator of the Riesz transforms associated to a Schr\"odinger operator $-\lap+V$, where $V$ satisfies some reverse H\"older inequality. The classes…
We establish an vector-valued interpolatory estimate between directional Haar projections and Riesz transforms.
We consider Riesz energy problems with radial external fields. We study the question of whether or not the equilibrium is the uniform distribution on a sphere. We develop general necessary as well as general sufficient conditions on the…
In this paper, we establish even order compact numerical schemes (4th-order, 6th-order, 8th-order, 10th-order) for Riesz derivatives by using the symmetrical fractional centred difference operator. Then we apply the derived 4th-order…
We introduce weighted Riesz bounded variation spaces defined on an open subset of the $n$-dimensional Euclidean space and use them to characterize weighted Sobolev spaces when the weight belongs to the Muckenhoupt class. As an application,…