The planar Orlicz Minkowski problem in the L1L1-sense

In this paper, we solve LpLp Minkowski problem for L1L1 data and all p<0p<0, and Orlicz Minkowski problem with two nonlinear terms in L1L1 sense. A byproduct is the Blaschke–Santaló inequality, which was previously established for only constant data, and now is shown to hold for L1L1 data.