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

Albanese, A.; Moscatelli, V.

Representations of the spaces

C^{\infty} (ℝ^{N}) \cap H^{k, p} (ℝ^{N})

Albanese, A. ; Moscatelli, V.

Studia Mathematica, Tome 141 (2000), p. 135-148 / Harvested from The Polish Digital Mathematics Library

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Résumé

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

Publié le : 2000-01-01

Zbl 0990.46014

EUDML-ID : urn:eudml:doc:216793

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     author = {A. Albanese and V. Moscatelli},
     title = {Representations of the spaces $C^$\infty$($\mathbb{R}$^N) $\cap$ H^{k,p}($\mathbb{R}$^N)$
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     journal = {Studia Mathematica},
     volume = {141},
     year = {2000},
     pages = {135-148},
     zbl = {0990.46014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv142i2p135bwm}
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Albanese, A.; Moscatelli, V. Representations of the spaces $C^∞(ℝ^N) ∩ H^{k,p}(ℝ^N)$
            . Studia Mathematica, Tome 141 (2000) pp. 135-148. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv142i2p135bwm/

Bibliographie

[000] [A] R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.

[001] [AA] A. A. Albanese, Montel subspaces of Fréchet spaces of Moscatelli type, Glasgow Math. J. 39 (1997), 345-350. | Zbl 0923.46011

[002] [AMM1] A. A. Albanese, G. Metafune and V. B. Moscatelli, Representations of the spaces $C^{m} (Ω) \cap H^{k, p} (Ω)$ , Math. Proc. Cambridge Philos. Soc. 120 (1996), 489-498.

[003] [AMM2] A. A. Albanese, G. Metafune and V. B. Moscatelli, Representations of the spaces $C^{m} (ℝ^{N}) \cap H^{k, p} ℝ^{N}$ , in: Functional Analysis (Trier, 1994), S. Dierolf, S. Dineen and P. Domański (eds.), Walter de Gruyter, 1996, 11-20.

[004] [AMM3] A. A. Albanese, G. Metafune and V. B. Moscatelli, On the spaces $C^{k} (ℝ) \cap L^{p} (ℝ)$ , Arch. Math. (Basel) 68 (1997), 228-232. | Zbl 0876.46022

[005] [AM] A. A. Albanese and V. B. Moscatelli, A method of construction of Fréchet spaces, in: Functional Analysis, P. K. Jain (ed.), Narosa Publishing House, New Delhi, 1998, 1-8. | Zbl 0949.46002

[006] [BB] K. D. Bierstedt and J. Bonet, Stefan Heinrich's density condition for Fréchet spaces and the characterization of distinguished Köthe echelon spaces, Math. Nachr. 135 (1988), 149-180. | Zbl 0688.46001

[007] [B] J. Bonet, Intersections of Fréchet Schwartz spaces and their duals, Arch. Math. (Basel) 68 (1997), 320-325. | Zbl 0916.46001

[008] [BD] J. Bonet and S. Dierolf, Fréchet spaces of Moscatelli type, Rev. Mat. Univ. Complut. Madrid 2 (suppl.) (1989), 77-92. | Zbl 0757.46001

[009] [BT] J. Bonet and J. Taskinen, Non-distinguished Fréchet function spaces, Bull. Soc. Roy. Sci. Liège 58 (1989), 483-490. | Zbl 0711.46001

[010] [DK] S. Dierolf and Khin Aye Aye, On projective limits of Moscatelli type, in: Functional Analysis (Trier, 1994), S. Dierolf, S. Dineen and P. Domański (eds.), Walter de Gruyter, 1996, 105-118. | Zbl 0902.46001

[011] [MT] P. Mattila and J. Taskinen, Remarks on bases in a Fréchet function space, Rev. Mat. Univ. Complut. Madrid 6 (1993), 93-99. | Zbl 0814.46005

[012] [M] V. B. Moscatelli, Fréchet spaces without continuous norms and without bases, Bull. London Math. Soc. 12 (1980), 63-66. | Zbl 0407.46002

[013] [S] R. T. Seeley, Extension of $C^{\infty}$ functions defined in a half space, Proc. Amer. Math. Soc. 15 (1964), 625-626. | Zbl 0127.28403

[014] [T1] J. Taskinen, A continuous surjection from the unit interval onto the unit square, Rev. Mat. Univ. Complut. Madrid 6 (1993), 101-120. | Zbl 0804.46027

[015] [T2] J. Taskinen, Examples of non-distinguished Fréchet spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. 14 (1989), 75-88. | Zbl 0632.46002

[016] [V1] M. Valdivia, Topics in Locally Convex Spaces, North-Holland Math. Stud. 67, 1982.

[017] [V2] M. Valdivia, A characterization of totally reflexive Fréchet spaces, Math. Z. 200 (1989), 327-346. | Zbl 0683.46008