Interpolation of weighted Orlicz spaces

摘要

The systematic treatment of spaces with weights began at the end of the fifties. The main field of application are the degenerate (elliptic) differential operators. There are only very few papers which are concerned with the interpolation theory of these spaces. In this paper, we use the interpolation method introduced by Gustavsson–Peetre [Stud. Math. 60 (1977) 33] to interpolate between weighted Lp-spaces. Here, we shall give some fundamental definitions and the basic interpolation results for the real interpolation method 〈X→〉ρ introduced in [Stud. Math. 60 (1977) 33] (see [SWJPAM 2 (1997) 29] and [SWJPAM 1 (2002) 71]). We also prove certain variants of two classical inequalities (Carlson’s inequality and Khinchine’s inequality) which will be needed later. We introduce our interpolation spaces 〈LΦ→(w)〉ρ and finally, we prove our main results.