Heat-flow monotonicity related to the Hausdorff-Young inequality
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چکیده
منابع مشابه
Heat-flow Monotonicity Related to the Hausdorff–young Inequality
It is known that if q is an even integer then the L(R) norm of the Fourier transform of a superposition of translates of a fixed gaussian is monotone increasing as their centres “simultaneously slide” to the origin. We provide explicit examples to show that this monotonicity property fails dramatically if q > 2 is not an even integer. These results are equivalent, upon rescaling, to similar sta...
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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: Bulletin of the London Mathematical Society
سال: 2009
ISSN: 0024-6093
DOI: 10.1112/blms/bdp073