Embedding theorems for Sobolev and Hardy-Sobolev spaces and estimates of Fourier transforms. (English) Zbl 1418.46016
Ann. Mat. Pura Appl. (4) 198, No. 2, 615-637 (2019); correction ibid. 201, No. 3, 1525-1530 (2022).
Summary: We prove embeddings of Sobolev and Hardy-Sobolev spaces into Besov spaces built upon certain mixed norms. This gives an improvement of the known embeddings into usual Besov spaces. Applying these results, we obtain Oberlin-type estimates of Fourier transforms for functions in Sobolev spaces \(W_1^1(\mathbb {R}^n)\).
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
Keywords:
embeddings; moduli of continuity; Sobolev spaces; Hardy spaces; mixed norms; Fourier transformsReferences:
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