Lp-dual affine surface area

According to the notion of Lp-affine surface area by Lutwak, in this paper, we introduce the concept of Lp-dual affine surface area. Further, we establish the affine isoperimetric inequality and the Blaschke–Santaló inequality for Lp-dual affine surface area. Besides, the dual Brunn–Minkowski inequality for Lp-dual affine surface area is presented.