A Schur multiplier characterization of coarse embeddability

Schur multiplier norm of product of matrices

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Coarse Embeddability Into

The main purposes of this paper are (1) To survey the area of coarse embeddability of metric spaces into Banach spaces, and, in particular, coarse embeddability of different Banach spaces into each other; (2) To present new results on the problems: (a) Whether coarse non-embeddability into l2 implies presence of expander-like structures? (b) To what extent l2 is the most difficult space to embe...

Coarse embeddability into Banach spaces

A Multilinear Schur Test and Multiplier Operators

A multilinear version of Schur’s test is obtained for products of L spaces and is used to derive boundedness for multilinear multiplier operators acting on Sobolev and Besov spaces.

On a conjecture of a bound for the exponent of the Schur multiplier of a finite $p$-group

Let $G$ be a $p$-group of nilpotency class $k$ with finite exponent $exp(G)$ and let $m=lfloorlog_pk floor$. We show that $exp(M^{(c)}(G))$ divides $exp(G)p^{m(k-1)}$, for all $cgeq1$, where $M^{(c)}(G)$ denotes the c-nilpotent multiplier of $G$. This implies that $exp( M(G))$ divides $exp(G)$, for all finite $p$-groups of class at most $p-1$. Moreover, we show that our result is an improvement...