Refined limiting imbeddings for Sobolev spaces of vector-valued functions
Copyright policy )Refined limiting imbeddings for Sobolev spaces of vector-valued functions
The authors consider vector-valued Sobolev, Besov, and Triebel-Lizorkin spaces of functions with values in a general Banach space; in general, these spaces may lack the UMD property. The authors prove a refined limiting embedding theorem of the Brézis-Wainger type in the critical case. The main result reads as follows: Theorem 3. Let \(1
- Polish Academy of Sciences Poland
- Schiller International University France
- Czech Academy of Sciences Czech Republic
- Institute of Mathematics Poland
- Academy of Sciences Library Czech Republic
critical imbeddings, Bessel potential spaces, Vector-valued functions, Lizorkin–Triebel spaces, Exponential Orlicz spaces, Triebel-Lizorkin spaces, Lorentz–Zygmund spaces, limiting imbeddings, envelopes, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Sharp inequalities, vector-valued functions, Lorentz-Zygmund spaces, exponencial Orlicz spaces, Spaces of vector- and operator-valued functions, sharp inequalities, Sobolev spaces, Besov spaces, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Function spaces arising in harmonic analysis, vector valued functions, Limiting imbeddings, Analysis, Envelopes
critical imbeddings, Bessel potential spaces, Vector-valued functions, Lizorkin–Triebel spaces, Exponential Orlicz spaces, Triebel-Lizorkin spaces, Lorentz–Zygmund spaces, limiting imbeddings, envelopes, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Sharp inequalities, vector-valued functions, Lorentz-Zygmund spaces, exponencial Orlicz spaces, Spaces of vector- and operator-valued functions, sharp inequalities, Sobolev spaces, Besov spaces, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Function spaces arising in harmonic analysis, vector valued functions, Limiting imbeddings, Analysis, Envelopes
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