In this paper, we establish the boundedness of commutators generated by weighted Lipschitz functions and Calderón-Zygmund singular integral operators on weighted Herz spaces.

We call (i?) 1 the Lie ring associated with R, and denote it by 9Î. The question of how far the properties of SR determine those of R is of considerable interest, and has been studied extensively for the case when R is an algebra, but little is known of the situation in general. In an earlier paper the author investigated the effect of the nilpotency of 9î upon the structure of R if R contains ...

Homomorphisms h:F ! * G are studied, where F is a free group and * G is the free product. In Part I, the conditions imposed on the homomorphism h relate to certain commutators in F . The method of proof is to obtain a topological realization of h, interpreting F as the fundamental group of a surface with boundary and * G as the fundamental group of a wedge of complexes. Standard general positio...

Initially, we set out to construct non-uniform ‘arithmetic’ lattices in Kac-Moody groups of rank 2 over finite fields, as constructed by Tits ([Ti1], [Ti2]) using the BruhatTits tree of a Tits system for such groups. This attempt succeeded, and in fact, the construction we used can be applied to higher rank Kac-Moody groups over sufficiently large finite fields, and their buildings (Theorem 1.7...