On the vector-valued Fourier transform and compatibility of operators

• Autorzy: In Sook Park
• Języki publikacji: EN

Abstrakty

EN

Let 𝔾 be a locally compact abelian group and let 1 < p ≤ 2. 𝔾' is the dual group of 𝔾, and p' the conjugate exponent of p. An operator T between Banach spaces X and Y is said to be compatible with the Fourier transform $F^{𝔾}$ if $F^{𝔾} ⊗ T: L_{p}(𝔾) ⊗ X → L_{p'}(𝔾') ⊗ Y $ admits a continuous extension $[F^{𝔾},T]:[L_{p}(𝔾),X] → [L_{p'}(𝔾'),Y]$. Let $ℱT_{p}^{𝔾}$ denote the collection of such T's. We show that $ℱT_{p}^{ℝ×𝔾} = ℱT_{p}^{ℤ×𝔾} = ℱT_{p}^{ℤⁿ×𝔾}$ for any 𝔾 and positive integer n. Moreover, if the factor group of 𝔾 by its identity component is a direct sum of a torsion-free group and a finite group with discrete topology then $ℱT_{p}^{𝔾} = ℱT_{p}^{ℤ}$.

Kategorie tematyczne

• 47L20: Operator ideals
• 43A25: Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 168
• Numer: 2
• Strony: 95-108

Daty

wydano

2005

Twórcy

autor

In Sook Park

• Division of Applied Mathematics, Korea Advanced Institute of Science and Technology, 373-1 Kuseong-dong, Yuseong-gu, Taejeon 305-701, Republic of Korea
• Next generation radio transmission research team, Mobile telecommunication group, Electronics and Telecommunications Research Institute, 161 Gajeong-dong, Yuseong-gu, Daejeon 305-350, Republic of Korea

Identyfikatory

DOI

10.4064/sm168-2-1