Annales Academię Scientiarum Fennicę
Mathematica
Volumen 36, 2011, 493-508

ON FOURNIER-GAGLIARDO MIXED NORM SPACES

Robert Algervik and Viktor I. Kolyada

Karlstad University, Department of Mathematics
Universitetsgatan 1, 651 88 Karlstad, Sweden; robealge 'at' kau.se

Karlstad University, Department of Mathematics
Universitetsgatan 1, 651 88 Karlstad, Sweden; viktor.kolyada 'at' kau.se

Abstract. We study mixed norm spaces V(Rⁿ) that arise in connection with embeddings of Sobolev spaces W₁¹(Rⁿ). We prove embeddings of V(Rⁿ) into Lorentz type spaces defined in terms of iterative rearrangements. Basing on these results, we introduce the scale of mixed norm spaces V^p(Rⁿ). We prove that V \subset V^p and we discuss some questions related to this embedding.

2010 Mathematics Subject Classification: Primary 46E30, 46E35; Secondary 26B35.

Key words: Mixed norms, rearrangements, embeddings, Sobolev spaces.

Reference to this article: R. Algervik and V.I. Kolyada: On Fournier-Gagliardo mixed norm spaces. Ann. Acad. Sci. Fenn. Math. 36 (2011), 493-508.

Full document as PDF file

doi:10.5186/aasfm.2011.3624

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