Related papers: Lipschitz and Triebel--Lizorkin spaces, commutator…

We give Littlewood-Paley type characterizations for Besov-Triebel-Lizorkin-type spaces $\mathscr B_{pq}^{s\tau},\mathscr F_{pq}^{s\tau}$ and Besov-Morrey spaces $\mathcal N_{uqp}^s$ on a special Lipschitz domain $\Omega\subset\mathbb R^n$:…

We consider the restricted Dirichlet-to-Neumann map $\Lambda^{U,V}_{g,A,q}$ for the wave equation with magnetic potential $A$ and scalar potential $q$, on an admissible Lorentzian manifold $(M, g)$ of dimension $n \geq 3$ with boundary.…

For $f$ analytic on the unit disc let $r_t(f)(z)=f(e^{it}z)$ and $f_r(z)=f(rz)$, rotations and dilations respectively. We show that for $f$ in the Bergman space $A^p$ and $0<\alpha\leq 1$ the following are equivalent. \begin{itemize}…

This paper continues the study of the mixed problem for the Laplacian. We consider a bounded Lipschitz domain $\Omega\subset \reals^n$, $n\geq2$, with boundary that is decomposed as $\partial\Omega=D\cup N$, $D$ and $N$ disjoint. We let…

Let $G:\mathbb{R\rightarrow R}$ be a continuous function. In the first part of this paper, we investigate sufficient conditions on $G$ such that \begin{equation*} \{G(f):f\in \dot{K}_{p,q}^{\alpha }F_{\beta }^{s}\}\subset…

In this paper we prove a parabolic Triebel-Lizorkin space estimate for the operator given by \[T^{\alpha}f(t,x) = \int_0^t \int_{{\mathbb R}^d} P^{\alpha}(t-s,x-y)f(s,y) dyds,\] where the kernel is \[P^{\alpha}(t,x) = \int_{{\mathbb R}^d}…

For a bounded Lipschitz domain $\Sigma$ in a Riemannian surface $M$ satisfying certain curvature condition, we prove that $$\mu_{3-\beta_1} \leq \lambda_{1},$$ where $\mu_k$ ($\lambda_k$ resp.) is the $k$-th Neumann (Dirichlet resp.)…

Let $(M,\rho,\mu)$ be a metric measure space satisfying the doubling, reverse doubling and non-collapsing conditions, and $\mathscr{L}$ be a self-adjoint operator on $L^2 (M, d\mu)$ whose heat kernel $p_t (x,y)$ satisfy the small-time…

The aim of this article is to give a complete solution to the problem of the bilinear decompositions of the products of some Hardy spaces $H^p(\mathbb{R}^n)$ and their duals in the case when $p<1$ and near to $1$, via wavelets, paraproducts…

This paper concerns Hodge-Dirac operators D = d + $\delta$ acting in L p ($\Omega$, {\lambda}) where $\Omega$ is a bounded open subset of R n satisfying some kind of Lipschitz condition, {\lambda} is the exterior algebra of R n , d is the…

The notion of $\Gamma$-symmetric space is a natural generalization of the classical notion of symmetric space based on $\Z_2$-grading of Lie algebras. In our case, we consider homogeneous spaces $G/H$ such that the Lie algebra $\g$ of $G$…

If $X$ is an analytic metric space satisfying a very mild doubling condition, then for any finite Borel measure $\mu$ on $X$ there is a set $N\subseteq X$ such that $\mu(N)>0$, an ultrametric space $Z$ and a Lipschitz bijection $\phi:N\to…

We show that for every complete metric space $M$ there exists another complete metric space $N$ of the same density character such that the curve-flat quotient of $N$ is isometric to $M$. Moreover, we show that if $M$ is compact and…

Motivated by the results of Korry and Kinnunen and Saksman, we study the behaviour of the discrete fractional maximal operator on fractional Hajlasz spaces, Hajlasz-Besov and Hajlasz-Triebel-Lizorkin spaces on metric measure spaces. We show…

In the 1990s, Kempf and his collaborators Mangano and Mann introduced a $D$-dimensional $(\beta,\beta')$-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length $(\triangle…

The triangular ratio metric is studied in subdomains of the complex plane and Euclidean $n$-space. Various inequalities are proven for it. The main results deal with the behavior of this metric under quasiconformal maps. We also study the…

Let $T$ be a compact, metrisable and strongly countable-dimensional topological space. Let $\mathcal{M}^T$ be the set of all metrics $d$ on $T$ compatible with its topology, and equip $\mathcal{M}^T$ with the topology of uniform…

We establish fractional Leibniz rules in weighted settings for nonnegative self-adjoint operators on spaces of homogeneous type. Using a unified method that avoids Fourier transforms, we prove bilinear estimates for spectral multiplier on…

Classical and non classical Besov and Triebel-Lizorkin spaces with complete range of indices are developed in the general setting of Dirichlet space with a doubling measure and local scale-invariant Poincar\'e inequality. This leads to Heat…

It is well known that in compact local Lipschitz neighborhood retracts in Euclidean space flat convergence for integer rectifiable currents amounts just to weak convergence. In the present paper we extend this result to integral currents in…