Agnieszka Kałamajska,
Katarzyna Pietruska-Pałuba
(2006)
We obtain interpolation inequalities for derivatives:
,
and their counterparts expressed in Orlicz norms:
||∇f||²(q,α) ≤ C||Φ₁(x,|f|,|∇(2)f|)||(p,β) ||Φ₂(x,|f|,|∇(2)f|)||(r,γ)where is the Orlicz norm relative to the function . The parameters p,q,r,α,β,γ and the Carathéodory functions Φ₁,Φ₂ are supposed to satisfy certain consistency conditions. Some of the classical Gagliardo-Nirenberg inequalities follow as a special case. Gagliardo-Nirenberg inequalities in logarithmic spaces...