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Fourier approximation and embeddings of Sobolev spaces

100%

Edmunds D. E., Moscatelli V. B.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS Introduction............................................................................................................ 5 1. Preliminaries............................................................................................................. 8 2. Embedding into $W^{m,p}(Ω)$ into $L^S(Ω)$ (n>1).......................................... 10 3. The case n = 1.......................................................................................................... 28 4. Embedding $W^{m,p}(Ω)$ into $L^φ(Ω)$............................................................ 29 5. Embedding $W^{m,p}_0(Ω)$ into $L^S(Ω)$ and $L^φ(Ω)$............................. 35 6. Applications to the type of the embedding.......................................................... 35 7. Unfortunate technicalities....................................................................................... 37 References.................................................................................................................... 46

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Representations of the spaces $C^∞(ℝ^N) ∩ H^{k,p}(ℝ^N)$

94%

Albanese A. A., Moscatelli V. B.

Studia Mathematica

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2000

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tom 142

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nr 2

135-148

EN

We give a representation of the spaces $C^∞(ℝ^N) ∩ H^{k,p}(ℝ^N)$ as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that $C^∞(ℝ^N) ∩ H^{k,2}(ℝ^N)$ is isomorphic to the sequence space $s^{ℕ} ∩ l^2(l^2)$, thereby showing that the isomorphy class does not depend on the dimension N if p=2.

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Bases in bornological spaces

38%

Moscatelli V. B.

Studia Mathematica

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1974

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tom 50

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nr 3

251-264

Ograniczanie wyników

2 Studia Mathematica

3 Moscatelli V. B.

1 Albanese A. A.

1 Edmunds D. E.

1 2000

1 1977

1 1974

Fourier approximation and embeddings of Sobolev spaces

Representations of the spaces $C^∞(ℝ^N) ∩ H^{k,p}(ℝ^N)$

Bases in bornological spaces