Related papers: Clarkson-Erd\"os-Schwartz Theorem on a Sector

We investigate the existence of compact Hausdorff spaces $X$ that are minimum with respect to $cX=K$ for some fixed covering operator $c$ and compact Hausdorff space $K$ with $cK=K$. Then, using the Yosida representation theorem, we show…

The main purpose of this paper is to give a vector lattice version of a Theorem by Burkholder about convergence of martingales. The proof is based on a vector lattice analogue of Austin's sample function theorem, proved recently by Grobler,…

In this paper, we establish a Minkowski-type inequality for weak Lebesgue space, which allows us to obtain a characterization of relative compactness in these spaces. Furthermore, we are the first to investigate the compactness results of…

In this paper we strengthen to Morrey-Lorentz spaces the famous trace principle introduced by Adams. More precisely, we show that Riesz potential $I_{\alpha}$ is continuous \begin{equation} \Vert I_{\alpha}f\Vert_{\mathcal{M}_{q,…

Let $(\mathbb{X} , d, \mu )$ be a proper metric measure space and let $\Omega \subset \mathbb{X}$ be a bounded domain. For each $x\in \Omega$, we choose a radius $0< \varrho (x) \leq \mathrm{dist}(x, \partial \Omega ) $ and let $B_x$ be the…

A series expansion for Heckman-Opdam hypergeometric functions $\varphi_\lambda$ is obtained for all $\lambda \in \mathfrak a^*_{\mathbb C}.$ As a consequence, estimates for $\varphi_\lambda$ away from the walls of a Weyl chamber are…

We investigate Riemannian manifolds $(M^n,g)$ whose curvature operator of the second kind $\mathring{R}$ satisfies the condition \begin{equation*} \alpha^{-1} (\lambda_1 +\cdots +\lambda_{\alpha}) > - \theta \bar{\lambda}, \end{equation*}…

We prove that a bounded linear Hilbert space operator has the unit circle in its essential approximate point spectrum if and only if it admits an orbit satisfying certain orthogonality and almost-orthogonality relations. This result is…

A classical theorem of Malykhin says that if $\{X_\alpha:\alpha\leq\kappa\}$ is a family of compact spaces such that $t(X_\alpha)\leq \kappa$, for every $\alpha\leq\kappa$, then $t\left( \prod_{\alpha\leq \kappa} X_\alpha \right)\leq…

We first prove a version of Tietze-Urysohn's theorem for proper functions taking values in non-negative real numbers defined on $\sigma$-compact locally compact Hausdorff spaces. As its application, we prove an extension theorem of proper…

In this note, we extend the well-known theorems of M. Riesz and Zygmund on conjugate functions as follows. Let $\Omega$ be a domain in $\mathbb C^n$. Suppose that $f=u+iv\in \mathcal O(\Omega)$ satisfies $v(z_0)=0$ for some $z_0\in \Omega$.…

A local Tb Theorem provides a flexible framework for proving the boundedness of a Calder\'on-Zygmund operator T. One needs only boundedness of the operator T on systems of locally pseudo-accretive functions \{b_Q\}, indexed by cubes. We…

We consider minimization problems of functionals given by the difference between the Willmore functional of a closed surface and its area, when the latter is multiplied by a positive constant weight $\Lambda$ and when the surfaces are…

The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…

Using recent characterizations of the compactness of composition operators on Hardy-Orlicz and Bergman-Orlicz spaces on the ball, we first show that a composition operator which is compact on every Hardy-Orlicz (or Bergman-Orlicz) space has…

The Rolling Ball Theorem asserts that given a convex body K in Euclidean space and having a smooth surface bd(K) with all principal curvatures not exceeding c>0 at all boundary points, K necessarily has the property that to each boundary…

We prove Rellich-Kondrachov type theorems on the half-space $\mathbb{H}^{N+1}=\{(y, x) \in \left.\mathbb{R} \times \mathbb{R}^N: y>0\right\}$ endowed with the general weighted measure $\mu_w:=y^c \phi(|z|) d z$, where $c \in \mathbb{R}$ and…

We extend the Theory of Computation on real numbers, continuous real functions, and bounded closed Euclidean subsets, to compact metric spaces $(X,d)$: thereby generically including computational and optimization problems over higher types,…

We present here an analogue of the Brian\c{c}on-Skoda theorem for a germ of an analytic space $Z$ at 0, such that $O_{Z,0}$ is Cohen-Macaulay, but not necessarily reduced. More precisely, we find a sufficient condition for membership of a…

A generalization of the classical Sard theorem in the plane is the following. Let $f$ be a function defined on a subset $A\subset{\mathbb R}^2$. If $f$ has modulus of continuity $\omega(r)\lesssim r^2$, then $f(A)\subset{\mathbb R}$ has…