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Hölder inequalities and sharp embeddings in function spaces of \(B_{pq}^ s\) and \(F_{pq}^ s\) type. (English) Zbl 0820.46030

Summary: Besides assertions on sharp embeddings of \(B^ s_{pq}\) and \(F^ s_{pq}\) we give necessary and sufficient conditions on the parameters \(s\), \(p\), \(q\), \(p_ 1\), \(q_ 1\), \(p_ 2\), \(q_ 2\) for the Hölder type inequalities \[ \| f\cdot g| B^ s_{pq}\|\leq c\| f| B^ s_{p_ 1 q_ 1}\| \| g| B^ s_{p_ 2 q_ 2}\|\quad\text{and}\quad \| f\cdot g| F^ s_{pq}\|\leq c\| f| F^ s_{p_ 1 q_ 1}\| \| g| F^ s_{p_ 2 q_ 2}\| \] to hold.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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