Tensor products and sums of 𝑝\mspace{1𝑚𝑢}-harmonic functions, quasiminimizers and 𝑝\mspace{1𝑚𝑢}-admissible weights

Abstract

The tensor product of two p p\mspace {1mu} -harmonic functions is in general not p p\mspace {1mu} -harmonic, but we show that it is a quasiminimizer. More generally, we show that the tensor product of two quasiminimizers is a quasiminimizer. Similar results are also obtained for quasisuperminimizers and for tensor sums. This is done in weighted R n \mathbf {R}^n with p p\mspace {1mu} -admissible weights. It is also shown that the tensor product of two p p\mspace {1mu} -admissible measures is p p\mspace {1mu} -admissible. This last result is generalized to metric spaces.