Related papers: Maximal and quadratic Gaussian Hardy spaces

For a metric space $X$ with a compatible measure $\mu$, Genevois and Tessera defined the Scaling Group of $(X,\mu)$ as the subgroup $\Gamma$ of $\mathbb{R}_{>0}$ of positive real numbers $\gamma$ for which there are quasi-isometries of $X$…

In this paper, we define and study a class $\mathcal{R}_{c}$ of norms on $L^{\infty}\left( \mathbb{T}\right) $, called $continuous\ rotationally\ symmetric \ norms$, which properly contains the class $\left \{ \left \Vert \cdot \right \Vert…

An analog of the Paley-Wiener isomorphism for the Hardy space with an invariant measure over infinite-dimensional unitary groups is described. This allows us to investigate on such space the shift and multiplicative groups, as well as,…

Suppose $D$ is a suitably admissible compact subset of $\mathbb{R}^k$ having a smooth boundary with possible zones of zero curvature. Let \mbox{$R(T,\theta,x)= N(T,\theta,x) - T^{k}\mathrm{vol}(D)$,} where $N(T,\theta,x)$ is the number of…

This work adresses the question of density of piecewise constant (resp. rigid) functions in the space of vector valued functions with bounded variation (resp. deformation) with respect to the strict convergence. Such an approximation…

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…

We introduce Gaussian-type measures on the manifold of all metrics with a fixed volume form on a compact Riemannian manifold of dimension $\geq 3$. For this random model we compute the characteristic function for the $L^2$ (Ebin) distance…

In this article, the authors introduce the Newton-Morrey-Sobolev space on a metric measure space $(\mathscr{X},d,\mu)$. The embedding of the Newton-Morrey-Sobolev space into the H\"older space is obtained if $\mathscr{X}$ supports a weak…

In this PhD thesis we discuss, develop and apply this fascinating theory connected to modern harmonic analysis. In particular we make new estimations of Vilenkin-Fourier coefficients and prove some new results concerning boundedness of…

The Hausdorff-Young inequality for Euclidean space, in its sharp form due to Beckner, gives an upper bound for the Fourier transform in terms of Lebesgue space norms, with an optimal constant. The extremizers have been identified by Lieb to…

This work concerns superharmonic perturbations of a Gaussian measure given by a special class of positive weights in the complex plane of the form $w(z) = \exp(-|z|^2 + U^{\mu}(z))$, where $U^{\mu}(z)$ is the logarithmic potential of a…

We consider an $L^2$-Wasserstein type distance $\rho$ on the configuration space $\Gamma_X$ over a Riemannian manifold $X$, and we prove that $\rho$-Lipschitz functions are contained in a Dirichlet space associated with a measure on…

We study weighted boundedness of Hardy-Littlewood-type maximal function involving Orlicz functions. We also obtain some sufficient conditions for the weighted boundedness of the Hardy-Littlewood maximal function of the upper-half plane.

Let $X$ be a ball quasi-Banach function space, $\alpha\in \mathbb{R}$ and $q\in(0,\infty)$. In this paper, the authors first introduce the Herz-type Hardy space $\mathcal{H\dot{K}}_{X}^{\alpha,\,q}({\mathbb {R}}^n)$, which is defined via…

We consider Muckenhoupt weights $w$, and define weighted Hardy spaces $H^p_{\mathcal{T}}(w)$, where $\mathcal{T}$ denotes a conical square function or a non-tangential maximal function defined via the heat or the Poisson semigroup generated…

Riemannian metrics on the unit ball of the quaternions, which are naturally associated with the reproducing kernel Hilbert spaces. We study the metric arising from the Hardy space in detail. We show that, in contrast to the one-complex…

Let $(X, d, \mu)$ be a space of homogeneous type, i.e. the measure $\mu$ satisfies doubling (volume) property with respect to the balls defined by the metric $d$. Let $L$ be a non-negative self-adjoint operator on $L^2(X)$. Assume that the…

This paper presents the Gaussian subordination framework to generate optimal one-sided approximations to multidimensional real-valued functions by functions of prescribed exponential type. Such extremal problems date back to the works of…

Maximal and atomic Hardy spaces Hp and HAp , are considered in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. It is…

In this paper, we study harmonic functions on metric measure spaces with Riemannian Ricci curvature bounded from below, which were introduced by Ambrosio-Gigli-Savar\'e. We prove a Cheng-Yau type local gradient estimate for harmonic…