Vector valued bilinear maximal operator and method of rotations

In this paper we obtain a bilinear analogue of Fefferman–Steinʼs vector valued inequality for classical Hardy–Littlewood maximal function. Also, we prove the boundedness of bilinear Hardy–Littlewood maximal operator from L p 1 ( R n ) × L p 2 ( R n ) → L 1 ( R n ) , where 1 p 1 + 1 p 2 = 1 , by applying the method of rotations.