A T(1)-THEOREM IN RELATION TO A SEMIGROUP OF OPERATORS AND APPLICATIONS TO NEW PARAPRODUCTS

作者：Bernicot Frederic^*

来源：Transactions of the American Mathematical Society, 2012, 364(11): 6071-6108.

DOI：10.1090/S0002-9947-2012-05609-1

• T(1)-theorem
• semigroup of operators
• paraproducts

In this work, we are interested in developing new directions of the famous T(1)-theorem. More precisely, we develop a general framework where we look to replace the John-Nirenberg space BMO (in the classical result) by a new BMOL, associated to a semigroup of operators (e-(tL))(t%26gt;0). These new spaces BMOL (including B MO) have recently appeared in numerous works in order to extend the theory of Hardy and B MO space to more general situations. Then we give applications by describing boundedness for a new kind of paraproduct, built on the considered semigroup. In addition we obtain a version of the classical T(1)-theorem for doubling Riemannian manifolds.

• 出版日期2012-11