A homomorphism theorem for bilinear multipliers

作者：Rodriguez Lopez Salvador^*

来源：Journal of the London Mathematical Society-Second Series, 2013, 88(2): 619-636.

DOI：10.1112/jlms/jdt043

In this paper, we prove an abstract homomorphism theorem for bilinear multipliers in the setting of locally compact Abelian (LCA) groups. We also provide some applications. In particular, we obtain a bilinear abstract version of de Leeuw%26apos;s theorem for bilinear multipliers of strong and weak types. We also obtain necessary conditions on bilinear multipliers on non-compact LCA groups, yielding boundedness for the corresponding operators on products of rearrangement invariant spaces. Our investigations extend some existing results in R-n to the framework of general LCA groups, and yield new boundedness results for bilinear multipliers in quasi-Banach spaces.

• 出版日期2013-10