Resumen de Semigroup commutators under differences, II.

Nick Th. Varopoulos

• This is the second instalment of my previous paper with the same title, [1]. This paper consists of two different parts. The first part is devoted to improvements of the results developed in [1]. These improvements are described in section 0.1 below and developed in sections 1 to 5, and 9 to 10; they are in fact technically distinct from [1] and rely on a systematic use of microlocalisation in the context of Hörmander-Weyl calculus. These paragraphs can therefore be read quite independently from [1].

  The second part studies a different problem and is, in its aim, fairly disjoint from [1]. This problem is explained in section 0.2 below and developed in sections 6 to 8. The techniques used however in sections 6 to 8 (and also in Section 10 which in its scope is attached to the first part) are very close to the techniques of [1].