Maximal and atomic Hardy spaces Hp and H A, 0 < p ≤ 1, 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 shown that Hp = H A with equivalent norms.

A relational structure is homomorphism-homogeneous if any homomorphism between its finite substructures extends to an endomorphism of the structure in question. In this note, we characterise all permutations on a finite set enjoying this property. To accomplish this, we switch from the more traditional view of a permutation as a set endowed with two linear orders to a different representation b...

In the year 1944 R. H. Bruck has described a very general construction method which he called the extension of a set by a quasigroup. We use it to construct a class of examples for LF-quasigroups in which the image of the map e(x) = x\x is a group. More generally, we consider the variety of quasigroups which is defined by the property that the map e is an endomorphism and its subvariety where t...

We study relational structures (especially graphs and posets) which satisfy the analogue of homogeneity but for homomorphisms rather than isomorphisms. The picture is rather different. Our main results are partial characterisations of countable graphs and posets with this property; an analogue of Fraı̈ssé’s Theorem; and representations of monoids as endomorphism monoids of such structures. ∗This...

The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In resulting framework, impulse response estimation problem is formulated as a regularized optimization defined on an infinite-dimensional RKHS consisting stable responses. consequent well-defined under central assumption that convolution operators restricted to are continuous line...

Using tensor categories, we present new constructions of several the exceptional simple Lie superalgebras with integer Cartan matrix in characteristic $p = 3$ and 5$ from complete classification modular indecomposable their subquotients over algebraically closed fields by Bouarroudj, Grozman, Leites 2009. Specifically, let $\mathbf{\alpha}_p$ denote kernel Frobenius endomorphism on additive gro...

Let G be a simple, simply connected algebraic group over an algebraically closed field k of characteristic p>0. σ:G→G surjective endomorphism such that the fixed point set G(σ) is Suzuki or Ree group. Then, let Gσ denote scheme-theoretic kernel σ. Using methods Jantzen and Bendel–Nakano–Pillen, we compute 1-cohomology for Frobenius kernels with coefficients in induced modules, H1(Gσ,H0(λ)), ext...

We prove a generalization of the fellow traveller property for certain type quasi-geodesics and use it to present three equivalent geometric formulations bounded reduction that this is preservation coarse median. then provide an affirmative answer question from Araújo Silva as whether every nontrivial uniformly continuous endomorphism hyperbolic group with respect visual metric satisfies Hölder...

Currently non-monotonic reasoning (NMR) is a promising approach to model features of common sense reasoning. In order to formalize NMR the research community has applied monotonic logics. The present paper furthers the study of one of the semantics useful in this formalization called p-stable. We introduce three different formats for normal programs: Negative normal programs, Restricted negativ...