Gagliardo–Nirenberg inequalities in weighted Orlicz spaces
Tom 173 / 2006
Studia Mathematica 173 (2006), 49-71 MSC: Primary 26D10; Secondary 46E35, 46E30. DOI: 10.4064/sm173-1-4
We derive inequalities of Gagliardo–Nirenberg type in weighted Orlicz spaces on $\mathbb R^n$, for maximal functions of derivatives and for the derivatives themselves. This is done by an application of pointwise interpolation inequalities obtained previously by the first author and of Muckenhoupt–Bloom–Kerman-type theorems for maximal functions.