2015/06/25 by The Anh Bui, Bui, The Anh, Jose M. Conde-Alonso +6
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #math.CA
paper · pdf · doi:10.48550/arxiv.1506.07752
arxiv created 2015/06/25 · openalex publication_date 2015/06/25 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let T be a multilinear integral operator which is bounded on certain products of Lebesgue spaces on \mathbb Rn. We assume that its associated kernel satisfies some mild regularity condition which is weaker than the usual Hölder continuity of those in the class of multilinear Calderón-Zygmund singular integral operators. In this paper, given a suitable multiple weight w, we obtain the bound for the weighted norm of multilinear operators T in terms of w. As applications, we exploit this result to obtain the weighted bounds for certain singular integral operators such as linear and multilinear Fourier multipliers and the Riesz transforms associated to Schrödinger operators on ℝn. Our results are new even in the linear case.