Related papers: Hardy spaces for semigroups with Gaussian bounds

Suppose that $\Omega$ is the open region in $\mathbb{R}^n$ above a Lipschitz graph and let $d$ denote the exterior derivative on $\mathbb{R}^n$. We construct a convolution operator $T $ which preserves support in $\bar{\Omega$}, is…

Let $p(\cdot):\ \mathbb R^n\to(0,1]$ be a variable exponent function satisfying the globally $\log$-H\"older continuous condition and $L$ a non-negative self-adjoint operator on $L^2(\mathbb R^n)$ whose heat kernels satisfying the Gaussian…

We treat two related trigonometric functional equations on semigroups. First we solve the $\mu$-sine subtraction law \[\mu(y) k(x \sigma(y))=k(x) l(y)-k(y) l(x), \quad x, y \in S,\] for $k, l : S\rightarrow \mathbb{C}$, where $S$ is a…

Calder\'on-Zygmund decompositions of functions have been used to prove weak-type (1,1) boundedness of singular integral operators. In many examples, the decomposition is done with respect to a family of balls that corresponds to some family…

In this paper we establish a rigidity property of holomorphic generators by using their local behavior at a boundary point $\tau$ of the open unit disk $\Delta$. Namely, if $f\in\mathrm{Hol}(\Delta,\mathbb{C})$ is the generator of a…

Let $\Omega$ be a domain in $\Ri^d$ with boundary $\Gamma$${\!,}$ $d_\Gamma$ the Euclidean distance to the boundary and $H=-\divv(C\,\nabla)$ an elliptic operator with $C=(\,c_{kl}\,)>0$ where $c_{kl}=c_{lk}$ are real, bounded, Lipschitz…

Let $K\subset \mathbb{R}^d$ be a post-critically finite (p.c.f.) self-similar set with Hausdorff dimension $s$, and $\mu$ be a self-similar probability measure supported on $K$. Let $H^{\alpha}_\mu$, $0<\alpha\le s$, be the Hausdorff…

Let $\Omega$ be homogeneous of degree zero, have vanishing moment of order one on the unit sphere $\mathbb {S}^{d-1}$($d\ge 2$). In this paper, our object of investigation is the following rough non-standard singular integral operator…

Let $\mathcal{X}$ be a metric space with doubling measure and $L$ a one-to-one operator of type $\omega$ having a bounded $H_\infty$-functional calculus in $L^2(\mathcal{X})$ satisfying the reinforced $(p_L, q_L)$ off-diagonal estimates on…

In this article we study the Ces\`{a}ro operator $$ \mathcal{C}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\zeta)\,d\zeta, $$ and its companion operator $\mathcal{T}$ on Hardy spaces of the upper half plane. We identify $\mathcal{C}$ and $\mathcal{T}$…

Let $\Lambda_s$ denote the inhomogeneous Lipschitz space of order $s\in(0,\infty)$ on $\mathbb{R}^n$. This article characterizes the distance $d(f, V)_{\Lambda_s}: = \inf_{g\in V} \|f-g\|_{\Lambda_s}$ from a function $f\in \Lambda_s$ to a…

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 work we extend the theory of the classical Hardy space $H^1$ to the rational Dunkl setting. Specifically, let $\Delta$ be the Dunkl Laplacian on a Euclidean space $\mathbb{R}^N$. On the half-space $\mathbb{R}_+\times\mathbb{R}^N$,…

We introduce new vanishing subspaces of the homogeneous H\"{o}lder space $\dot{C}^{0,\omega}(X,Y)$ in the generality of a doubling modulus $\omega$ and normed spaces $X$ and $Y.$ For many couples $X,Y,$ we show these vanishing subspaces to…

Let $\kappa \ge 2, \lambda > 1$ and define the multilinear Littlewood-Paley-Stein operators by $$g_{\lambda,\mu}^*(\vec{f})(x) = \bigg(\iint_{\mathbb{R}^{n+1}_{+}} \vartheta_t(x, y) \bigg|\int_{\mathbb{R}^{n \kappa}} s_t(y,\vec{z})…

We use algebraic techniques to study homological filling functions of groups and their subgroups. If $G$ is a group admitting a finite $(n+1)$--dimensional $K(G,1)$ and $H \leq G$ is of type $F_{n+1}$, then the $n^{th}$--homological filling…

In this paper we consider a large class of fully nonlinear integro-differential equations. The class of our nonlocal operators we consider is not spatial homogeneous and we put mild assumptions on its kernel near zero. We prove the H\"older…

Let $\mathscr{C}$ be a symmetric tensor category of moderate growth, and let $\mathcal{H}\subseteq\mathcal{G}$ be algebraic groups in $\mathscr{C}$. We prove that the homogeneous space $\mathcal{G}/\mathcal{H}$ exists and is of finite type…

A subalgebra $A$ of the algebra $B(\mathcal{H})$ of bounded linear operators on a separable Hilbert space $\mathcal{H}$ is said to be catalytic if every transitive subalgebra $\mathcal{T}\subset B(\mathcal{H})$ containing it is strongly…

Let $T_{\Omega,\alpha}$ be the homogeneous fractional integral operator defined as \begin{equation*} T_{\Omega,\alpha}f(x):=\int_{\mathbb R^n}\frac{\Omega(x-y)}{|x-y|^{n-\alpha}}f(y)\,dy, \end{equation*} and the related fractional maximal…