Abstract
AbstractIn this paper we continue the study of the spaces $${\mathcal O}_{M,\omega }({\mathbb R}^N)$$
O
M
,
ω
(
R
N
)
and $${\mathcal O}_{C,\omega }({\mathbb R}^N)$$
O
C
,
ω
(
R
N
)
undertaken in Albanese and Mele (J Pseudo-Differ Oper Appl, 2021). We determine new representations of such spaces and we give some structure theorems for their dual spaces. Furthermore, we show that $${\mathcal O}'_{C,\omega }({\mathbb R}^N)$$
O
C
,
ω
′
(
R
N
)
is the space of convolutors of the space $${\mathcal S}_\omega ({\mathbb R}^N)$$
S
ω
(
R
N
)
of the $$\omega $$
ω
-ultradifferentiable rapidly decreasing functions of Beurling type (in the sense of Braun, Meise and Taylor) and of its dual space $${\mathcal S}'_\omega ({\mathbb R}^N)$$
S
ω
′
(
R
N
)
. We also establish that the Fourier transform is an isomorphism from $${\mathcal O}'_{C,\omega }({\mathbb R}^N)$$
O
C
,
ω
′
(
R
N
)
onto $${\mathcal O}_{M,\omega }({\mathbb R}^N)$$
O
M
,
ω
(
R
N
)
. In particular, we prove that this isomorphism is topological when the former space is endowed with the strong operator lc-topology induced by $${\mathcal L}_b({\mathcal S}_\omega ({\mathbb R}^N))$$
L
b
(
S
ω
(
R
N
)
)
and the last space is endowed with its natural lc-topology.
Funder
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis
Reference37 articles.
1. Adams, R.A.: Sobolev Spaces. Academic Press, London (1975)
2. Albanese, A.A., Mele, C.: Multipliers on $${\cal{S}}_{\omega }({\mathbb{R}}^N)$$. J. Pseudo-Differ. Oper. Appl. 12, 35 (2021)
3. Bargetz, C., Ortner, N.: Characterization of L. Schwartz’ convolutor and multiplier spaces $${\cal{O}}^{\prime }_C$$ and $${\cal{O}}_M$$ by the short-time Fourier transform. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM (2014) 108, 833–847 (2014)
4. Barros-Neto, J.: An Introduction to the Theory of Distributions. Marcel Dekker Inc, New York (1973)
5. Betancor, J.J., Fernández, C., Galbis, A.: Beurling ultradistributions of $$L_p$$-growth. J. Math. Anal. Appl. 279, 246–265 (2003)
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