Related papers: A Remark on "Two-Sided" Monotonicity Condition: An…

We prove the optimality of the hypotheses guaranteeing the $L^p$-boundedness for the Cauchy-Leray integral in $\mathbb C^n$, $n\geq 2$, obtained in [LS-4]. Two domains, both elementary in nature, show that the geometric requirement of…

We consider classical solutions to $-\Delta u = f(u)$ in half-spaces, under homogeneous Dirichlet boundary conditions. We prove that any positive solution is strictly monotone increasing in the direction orthogonal to the boundary, provided…

For $p\in [1,\infty)$, we show that every unital $L^p$-operator algebra contains a unique maximal $C^*$-subalgebra, which is always abelian if $p\neq 2$. Using this, we canonically associate to every unital $L^p$-operator algebra $A$ an…

In two preceding articles, we studied the problem of the existence and uniqueness of a solution to some general BSDE on manifolds. In these two articles, we assumed some Lipschitz conditions on the drift $f(b,x,z)$. The purpose of this…

We prove a compactness criterion for asymptotic $L_p$ spaces over arbitrary measure spaces. Total boundedness is characterized by almost equiboundedness together with total boundedness in $L_p$ of all truncations. This gives a…

We give the most general conditions to date which lead to uniqueness of the general relativistic Hamiltonian. Namely, we show that all spatially covariant generalizations of the scalar constraint which extend the standard one while…

We obtain several generalizations the Hellinger theorem about $l^2$ solutions of difference equations: instead of second order equations and $ l^2$-solutions, we consider second-order equations with matrix coefficients and their solutions…

In the abstract of [1] we read: "We obtain so far unproved properties of a ratio involving a classof Hermite and parabolic cylinder functions." However, we explain how some of the main results in that paper were already proved in [2],…

We give a family of congruences for the binomial coefficients ${kp-1\choose p-1}$ in terms of multiple harmonic sums, a generalization of the harmonic numbers. Each congruence in this family (which depends on an additional parameter $n$)…

We prove a local analogue of a theorem of J. Martinet about the absolute norm of the relative discriminant ideal of an extension of number fields. The result can be seen as a statement about 2-primary units. We also prove a similar…

The aim of this paper is to give an overview of some inequalities about $L^p$-norms ($p= 1$ or $p= 2$) of harmonic (periodic) and non-harmonic trigonometric polynomials. Among the material covered, we mention Ingham's Inequality about 2…

The aim of this study is to provide a perspective to help understand the singular average operator over polynomial hypersurfaces. In particular, this perspective will provide brevity and the possibility of generalizing previous results…

Given an odd prime p, we prove a congruence on the p-residue of the Fermat quotient q_p(a) in base a with 0<a<p, which arises from a generalization of the Voronoi congruences and from some other congruences on sums and weighted sums of…

Let $F_{p}(x) =L( t^{p}f(t)) =\int_{0}^{\infty }t^{p}f(t) e^{-xt}dt$ converge on $(0,\infty)$ for $p\in \mathbb{N}_{0}=\mathbb{N}\cup{0}$, where $f(t)$ is positive on $(0,\infty)$. In a recent paper [Z.-H. Yang, A complete monotonicity…

This paper explores two generalizations of the classical Aubin-Lions Lemma. First we give a sufficient condition to commute weak limit and multiplication of two functions. We deduce from this criteria a compactness Theorem for degenerate…

We introduce the classical Jung theorem and fixed point theorems and prove similar ones for $p$-uniformly convex spaces.

Consider a complete asymptotically flat 3-manifold $M$ with non-negative scalar curvature and non-empty minimal boundary $\Sigma$. Fix a number $1 < p < 3$. We derive monotone quantities for $p$-harmonic functions on $M$ which become…

We prove $L^p$-mass concentration properties of Laplace eigenfunctions away from their nodal sets, extending a recent result in \cite{GM3} to all dimensions, and giving a slight refinement of a result in \cite{JN}. As a consequence, we are…

We show that for a convex function the following, rather modest conditions, are equivalent to monotonicity under local operations and classical communication. The conditions are: 1)invariance under local unitaries, 2) invariance under…

Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to…