齐型空间上的分数次积分算子

An equivalent definition of fractional integral on spaces of homogeneous type is given.The behavior of the fractional integral operator in Triebel-Lizorkin space is discussed.     

Pseudo-Riemannian almost quaternionic homogeneous spaces with irreducible isotropy

We show that pseudo-Riemannian almost quaternionic homogeneous spaces with index 4 and an \(\mathbb {H}\)-irreducible isotropy group are locally isometric to a pseudo-Riemannian quaternionic Kähler symmetric space if the dimension is at least 16. In dimension 12 we give a non-symmetric example.     

Periods of principal homogeneous spaces of algebraic tori

A generic torsor of an algebraic torus S over a field F is the generic fiber of a S-torsor P → T, where P is a quasi-trivial torus containing S as a subgroup and T = P/S. The period of a generic S-torsor over a field extension K/F, i.e., the order of the class of the torsor in the group H ^p1(K, S) does not depend on the choice of a generic torsor. In the paper we compute the period of a generic torsor of S in terms of the character lattice of the torus S.     

粗糙核多线性分数次积分算子在Morrey-Herz空间中的有界性

研究两类带粗糙核的多线性分数次积分算子,用转化为相应的截断算子来研究的方法,得出它们是从M（K）α,λp1,q1）空间到M（K）α,λp1,q1）空上的有界算子,把前人Herz空间此类算子的有界性推广到Herz-Morrey空间.     

On embeddings of certain spherical homogeneous spaces in prime characteristic

Let $ \mathcal{G} $ be a reductive group over an algebraically closed field of characteristic p?>?0. We study embeddings of homogeneous $ \mathcal{G} $ -spaces that are induced from the G?×?G-space G, G a suitable reductive group, along a parabolic subgroup of $ \mathcal{G} $ . We give explicit formulas for the canonical divisors and for the divisors of B-semi-invariant functions. Furthermore, we show that, under certain mild assumptions, any (normal) equivariant embedding of such a homogeneous space is canonically Frobenius split compatible with certain subvarieties and has an equivariant rational resolution by a toroidal embedding. In particular, all these embeddings are Cohen?CMacaulay. Examples are the G?×?G-orbits in normal reductive monoids with unit group G. Further examples are the open $ \mathcal{G} $ -orbits of the well known determinantal varieties and the varieties of (circular) complexes. Finally, we study the Gorenstein property for the varieties of circular complexes and for a related reductive monoid.     

Existence of non-isotropic conjugate points on rank one normal homogeneous spaces

We give a positive answer to the Chavel’s conjecture (J Differ Geom 4:13–20, 1970): a simply connected rank one normal homogeneous space is symmetric if any pair of conjugate points are isotropic. It implies that all simply connected rank one normal homogeneous space with the property that the isotropy action is variational complete is a rank one symmetric space.     

Chebyshev centers proximinality and farthest points in strong normed almost linear spaces

Some results from the theory of best (or best simultaneous) approximation in a normed linear space have been extended to a normed almost linear space [strong normed almost linear space].     

Common fixed points of almost generalized contractive mappings in ordered metric spaces

The existence theorems of common fixed points for two weakly increasing mappings satisfying an almost generalized contractive condition in ordered metric spaces are proved. Some comparative example are constructed which illustrate the values of the obtained results in comparison to some of the existing ones in literature.     

The Ruziewicz problem and distributing points on homogeneous spaces of a compact Lie group

LetG be any compact non-commutative simple Lie group not locally isomorphic to SO(3). We present a generalization of a theorem of Lubotzky, Phillips and Sarnak on distributing points on the sphere S² (or S³) to any homogeneous space ofG, in particular, to all higher dimensional spheres. Our results can also be viewed as a quantitative solution to the generalized Ruziewicz problem for any homogeneous space ofG. Partially supported by DMS-0070544 and DMS-0333397.     

Distributions on homogeneous spaces

A survey of results and ideas in the general analytic treatment of the theory of distributions on homogeneous spaces is presented.Translated from Itogi Nauki i Tekhniki. Problemy Geometrii, Vol. 8, pp. 5–24, 1977.     

Prime ideals and prime radicals in near-rings

This paper investigates conditions under which a prime ideal is completely prime and conditions for which every prime ideal in a near-ring is completely prime. Various implications of these conditions are examined with respect to the associated radicals.     

Weighted norm inequalities for the maximal singular integral operators on spaces of homogeneous type

Weighted norm inequalities with general weights are established for the maximal singular integral operators on spaces of homogeneous type, when the kernel satisfies a Hörmander regularity condition on one variable and a Hölder regularity condition on the other variable.     

Some results on almost principal element lattices

In this paper, we explore locally principal element lattices in terms of primary, semiprimary and prime power elements.     

Semigroup actions on homogeneous spaces

LetG be a connected semi-simple Lie group with finite center andS⊄G a subsemigroup with interior points. LetG/L be a homogeneous space. There is a natural action ofS onG/L. The relationx≤y ify ∈Sx, x, y ∈G/L, is transitive but not reflexive nor symmetric. Roughly, a control set is a subsetD ⊄G/L, inside of which reflexivity and symmetry for ≤ hold. Control sets are studied inG/L whenL is the minimal parabolic subgroup. They are characterized by means of the Weyl chambers inG meeting intS. Thus, for eachw ∈W, the Weyl group ofG, there is a control setD _w .D ₁ is the only invariant control set, and the subsetW(S)={w:D _w =D ₁} turns out to be a subgroup. The control sets are determined byW(S)/W. The following consequences are derived: i)S=G ifS is transitive onG/H, i.e.Sx=G/H for allx ∈G/H. HereH is a non discrete closed subgroup different fromG andG is simple. ii)S is neither left nor right reversible ifS #G iii)S is maximal only if it is the semigroup of compressions of a subset of some minimal flag manifold. Research partially supported by CNPq grant n^o 50.13.73/91-8     

Prime and prime power divisibility of Catalan numbers

For any prime p, the sequence of Catalan numbers

$\text{a}{}_{\mathrm{n}}\text{=}\text{1}\text{n}\text{2n?2}\text{n?1}$

is divided by the a_n prime to p into blocks B_k(k > 0) of a_n divisible by p. The lengths and positions of the B_k are determined. Additional results are obtained on prime power divisibility of Catalan numbers.