On the vector valued Hausdorff-Young inequality
نویسندگان
چکیده
منابع مشابه
A Hausdorff-young Inequality for Measured Groupoids
The classical Hausdorff-Young inequality for locally compact abelian groups states that, for 1 ≤ p ≤ 2, the L-norm of a function dominates the L-norm of its Fourier transform, where 1/p + 1/q = 1. By using the theory of non-commutative L-spaces and by reinterpreting the Fourier transform, R. Kunze (1958) [resp. M. Terp (1980)] extended this inequality to unimodular [resp. non-unimodular] groups...
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Let G be a locally compact abelian group with dual group Ĝ. The Hausdorff–Young theorem states that if f ∈ Lp(G), where 1 ≤ p ≤ 2, then its Fourier transform Fp(f) belongs to Lq(Ĝ) (where 1 p + 1 q = 1) and ||Fp(f)||q ≤ ||f ||p. Kunze and Terp extended this to unimodular and locally compact groups, respectively. We further generalize this result to an arbitrary locally compact quantum group G b...
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ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 1998
ISSN: 0004-2080
DOI: 10.1007/bf02385664