Bilinear Spherical Maximal Functions of Product Type

In this paper we introduce and study a bilinear spherical maximal function of product type in the spirit Calderón–Zygmund theory. This operator is different from considered by Geba et al. (Math Res Lett 20(4):675–694, 2013). We deal with lacunary full versions operator, prove weighted estimates respect to genuine weights beyond Banach range. Our results are implied sharp sparse domination for both operators, following ideas Lacey (J Anal Math 139(2):613–635, 2019). case also use interpolation analytic families operators address boundedness whole range tuples.