On a trilinear form related to the Carleson theorem

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:405

Article

Kovac, Vjekoslav

关键词: Multilinear form;    Bilinear Hilbert transform;    Carleson theorem;    Walsh function;    Bellman function;   

DOI  :  10.1016/j.jmaa.2013.04.008

来源: Elsevier

【 摘 要 】

Demeter and Thiele introduced the two-dimensional bilinear Hilbert transform in Demeter and Thiele (2010) [3] and showed that the Carleson operator can be identified in particular instances of the corresponding trilinear form. Demeter considered the Walsh model of one such form in Demeter (2012) [2], in relation to the discussion of the Walsh-Carleson theorem. We prove boundedness of this trilinear form for a single triple of exponents at the boundary of the previously established range. For this purpose, we adapt the multilinear Bellman function technique from Kovac (2011) [5] to the one-and-a-half-dimensional time-frequency space. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free