Related papers: Endpoint estimates for higher order Gaussian Riesz…

We establish pointwise ergodic theorems for operators of Radon type along subsets of prime numbers of the form $\big\{\{ \varphi_1(n)\} < \psi(n)\big\}$. We achieve this by proving $\ell^p(\mathbb{Z})$ boundedness of $r$-variations, where…

Analytic functions in the Hardy class $H^2$ over the upper half-plane $\mathbb{H}_+$ are uniquely determined by their values on any curve $\Gamma$ lying in the interior or on the boundary of $\mathbb{H}_+$. The goal of this paper is to…

In a previous paper the boundedness properties of Riesz Potentials, Bessel potentials and Fractional Derivatives were studied in detail on Gaussian Besov-Lipschitz spaces $B_{p,q}^{\alpha}(\gamma_d)$. In this paper we will continue our…

We generalize the notion of Erd\H{o}s-Ginzburg-Ziv constants -- along the same lines we generalized in earlier work the notion of Davenport constants -- to a ``higher degree" and obtain various lower and upper bounds. These bounds are…

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…

In this paper we first study the generalized weighted Hardy spaces $H^p_{L,w}(X)$ for $0<p\le 1$ associated to nonnegative self-adjoint operators $L$ satisfying Gaussian upper bounds on the space of homogeneous type $X$ in both cases of…

Indefinite causal orders have been shown to enable a precision of inverse square N in quantum parameter estimation, where N is the number of independent processes probed in an experiment. This surpasses the widely accepted ultimate quantum…

We investigate the thermodynamic limit of the circular long-range Riesz gas, a system of particles interacting pairwise through an inverse power kernel. We show that after rescaling, so that the typical spacing of particles is of order $1$,…

We show that if $X$ is a limit of $n$-dimensional Riemannian manifolds with Ricci curvature bounded below and $\gamma$ is a limit geodesic in $X$ then along the interior of $\gamma$ same scale measure metric tangent cones $T_{\gamma(t)}X$…

Let (E,H,mu) be an abstract Wiener space and let D_V := VD, where D denotes the Malliavin derivative and V is a closed and densely defined operator from H into another Hilbert space G. Given a bounded operator B on G, coercive on the…

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…

The main result of this work is the proof of the boundedness of the Ornstein-Uhlenbeck semigroup $ \{T_t \}_{t\geq 0} $ in $ {\mathbb R}^d $ on Gaussian variable Lebesgue spaces under a condition of regularity on $p(\cdot)$ following…

We derive a dyadic model operator for the Riesz vector. We show linear upper $L^p$ bounds for $1 < p < \infty$ between this model operator and the Riesz vector, when applied to functions with values in Banach spaces. By an upper bound we…

We consider spherical Riesz means of multiple Fourier series and some generalizations. While almost everywhere convergence of Riesz means at the critical index $(d-1)/2$ may fail for functions in the Hardy space $h^1(\mathbb T^d)$, we prove…

Canonical formulation of higher order theory of gravity can only be accomplished associating additional degrees of freedom, which are extrinsic curvature tensor. Consequently, to match Cauchy data with the boundary data, terms in addition…

Let $\mathbb{H}^{n}$ be the Heisenberg group. For $0 \leq \alpha < Q=2n+2$ and $N \in \mathbb{N}$ we consider exponent functions $p(\cdot) : \mathbb{H}^{n} \to (0, +\infty)$, which satisfies H\"older conditions, such that $\frac{Q}{Q+N} <…

Higher-order spacing ratios are investigated analytically using a Wigner-like surmise for Gaussian ensembles of random matrices. For $k$-th order spacing ratio $(r^{(k)}$, $k>1)$ the matrix of dimension $2k+1$ is considered. A universal…

In this paper, we establish some Strichartz estimates for orthonormal functions and probabilistic convergence of density functions related to compact operators on manifolds. Firstly, we present the suitable bound of $\int_{a\leq|s|\leq…

An algebraic Riccati equation for linear operators is studied, which arises in systems theory. For the case that all involved operators are unbounded, the existence of infinitely many selfadjoint solutions is shown. To this end, invariant…

We study the tail behaviour of measurable functions under generalized Riesz-type operators in the framework of Grand Lebesgue Spaces. By exploiting the connection between the growth of $L^p$ norms and the Young--Fenchel transform, we derive…