Vector valued bilinear maximal operator and method of rotations (Q549769)

This paper deals with the vector valued inequality for the bilinear Hardy-Littlewood maximal function. The main result, which is the bilinear analogue of the classical result due to \textit{C. Fefferman} and \textit{E. M. Stein} [Am. J. Math. 93, 107--115 (1971; Zbl 0222.26019)], is obtained in dimension one and it is a consequence of the boundedness of the bilinear maximal operator proved by \textit{M. Lacey} [Ann. Math. (2) 151, No. 1, 35--57 (2000; Zbl 0967.47031)]. The work is completed with the boundedness of higher-dimensional bilinear maximal operators from \(L^{p_1}(\mathbb{R}^n) \times L^{p_2}(\mathbb{R}^n) \longrightarrow L^{1}(\mathbb{R}^n)\), where \(\frac{1}{p_1}+ \frac{1}{p_2}=1\), by applying the method of rotations.