In this paper we prove that minimal 3-spheres of CR type with constant sectional curvature c in the complex projective space CPn are all equivariant and therefore the immersion is rigid. The curvature c of the sphere should be c = 1/(m2-1) for some integer m≥ 2, and the full dimension is n = 2m2-3. An explicit analytic expression for such an immersion is given.

In this paper we investigate the boundedness on Hardy spaces for the higher order commutator Tb, m generated by the BMO function b and fractional integral type operator Tτ, and establish the boundness theorems for Tτb, m from Hp1.q1.sb, m to Lp2 and to Hp2 (0 < p1 ≤ 1), and from H Ka. p1.sq1, b, m to Ka.p2q2 and to H Ka. p2q2, respectively, for certain ranges of α, p1, q1, p2, q2 and s.

In this paper we investigate when negative definite functions on commutative hypergroups satisfy the Schoenberg criterion.

A generalization of the Pastijn product is introduced so that, on the level of e-varieties and pseudoe-varieties, this product and the regular semidirect product by completely simple semigroups ‘almost always’ coincide. This is applied to give a model of the bifree objects in every e-variety formed as a regular semidirect product of a variety of inverse semigroups by a variety of completely simple semigroups that is not a group variety.

In this paper, we investigate Volterra spaces and relevant topological properties. New characterizations of weakly Volterra spaces are provided. An analogy of the Banach category theorem in terms of Volterra properties is obtained. It is shown that every weakly Volterra homogeneous space is Volterra, and there are metrizable Baire spaces whose hyperspaces of nonempty compact subsets endowed with the Vietoris topology are not weakly Volterra.

The purpose of this paper is to prove strong type inequalities with pairs of related weights for commutators of one-sided singular integrals (given by a Calderón-Zygmund kernel with support in (-∞, 0)) and the one-sided discrete square function. The estimate given by C. Segovia and J. L. Torrea is improved for these one-sided operators giving a wider class of weights for which the inequality holds.

Finite innately transitive permutation groups include all finite quasiprimitive and primitive permutation groups. In this paper, results in the theory of quasiprimitive and primitive groups are generalised to innately transitive groups, and in particular, we extend results of Praeger and Shalev. Thus we show that innately transitive groups possess parameter bounds which are similar to those for primitive groups. We also classify the innately transitive types of quotient actions of innately transitive groups.

Let ℋ(m;t) be the finite-dimensional odd Hamiltonian superalgebra over a field of prime characteristic. By determining ad-nilpotent elements in the even part, the natural filtration of ℋ (m;t) is proved to be invariant in the following sense: If ϕ: ℋ (m;t) → ℋ (m′t′) is an isomorphism then ϕ(ℋ(m;t)i) = ℋ (m′ t′) i for all i ≥ –1. Using the result, we complete the classification of odd Hamiltonian superalgebras. Finally, we determine the automorphism group of the restricted odd Hamiltonian superalgebra and give further properties.

In this paper, we show some results involving classical geometric concepts. For example, we characterize rotundity and Efimov-Stechkin property by mean of faces of the unit ball. Also, we prove that every almost locally uniformly rotund Banach space is locally uniformly rotund if its norm is Fréchet differentiable. Finally, we also provide some theorems in which we characterize the (strongly) exposed points of the unit ball using renormings.

The conjugacy classes of so-called special involutions parameterize the constituents of the action of a finite Coxeter group on the cohomology of the complement of its complexified hyperplane arrangement. In this note we give a short intrinsic characterisation of special involutions in terms of so-called bulky parabolic subgroups.