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

• Autorzy: A. A. Albanese , V. B. Moscatelli
• Języki publikacji: EN

Abstrakty

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2000
• Tom: 142
• Numer: 2
• Strony: 135-148

Daty

wydano

2000

otrzymano

1999-02-19

poprawiono

2000-06-12

Twórcy

autor

A. A. Albanese

• Dipartimento di Matematica 'E. De Giorgi', Università - C.P. 193, 73100 Lecce, Italy

autor

V. B. Moscatelli

• Dipartimento di Matematica 'E. De Giorgi', Università - C.P. 193, 73100 Lecce, Italy

Bibliografia

• [A] R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
• [AA] A. A. Albanese, Montel subspaces of Fréchet spaces of Moscatelli type, Glasgow Math. J. 39 (1997), 345-350.
• [AMM1] A. A. Albanese, G. Metafune and V. B. Moscatelli, Representations of the spaces $C^m(Ω) ∩ H^{k,p}(Ω)$, Math. Proc. Cambridge Philos. Soc. 120 (1996), 489-498.
• [AMM2] A. A. Albanese, G. Metafune and V. B. Moscatelli, Representations of the spaces $C^m(ℝ^N) ∩ H^{k,p}ℝ^N$, in: Functional Analysis (Trier, 1994), S. Dierolf, S. Dineen and P. Domański (eds.), Walter de Gruyter, 1996, 11-20.
• [AMM3] A. A. Albanese, G. Metafune and V. B. Moscatelli, On the spaces $C^k(ℝ) ∩ L^p(ℝ)$, Arch. Math. (Basel) 68 (1997), 228-232.
• [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.
• [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.
• [B] J. Bonet, Intersections of Fréchet Schwartz spaces and their duals, Arch. Math. (Basel) 68 (1997), 320-325.
• [BD] J. Bonet and S. Dierolf, Fréchet spaces of Moscatelli type, Rev. Mat. Univ. Complut. Madrid 2 (suppl.) (1989), 77-92.
• [BT] J. Bonet and J. Taskinen, Non-distinguished Fréchet function spaces, Bull. Soc. Roy. Sci. Liège 58 (1989), 483-490.
• [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.
• [MT] P. Mattila and J. Taskinen, Remarks on bases in a Fréchet function space, Rev. Mat. Univ. Complut. Madrid 6 (1993), 93-99.
• [M] V. B. Moscatelli, Fréchet spaces without continuous norms and without bases, Bull. London Math. Soc. 12 (1980), 63-66.
• [S] R. T. Seeley, Extension of $C^∞$ functions defined in a half space, Proc. Amer. Math. Soc. 15 (1964), 625-626.
• [T1] J. Taskinen, A continuous surjection from the unit interval onto the unit square, Rev. Mat. Univ. Complut. Madrid 6 (1993), 101-120.
• [T2] J. Taskinen, Examples of non-distinguished Fréchet spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. 14 (1989), 75-88.
• [V1] M. Valdivia, Topics in Locally Convex Spaces, North-Holland Math. Stud. 67, 1982.
• [V2] M. Valdivia, A characterization of totally reflexive Fréchet spaces, Math. Z. 200 (1989), 327-346.