On the Constant in a Transference Inequality for the Vector-valued Fourier Transform

Dion Gijswijt; Jan van Neerven

On the Constant in a Transference Inequality for the Vector-valued Fourier Transform

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Abstract

The standard proof of the equivalence of Fourier type on R^d and on the torus T^d is usually stated in terms of an implicit constant, defined as the minimum of a sum of powers of sinc functions. In this note we compute this minimum explicitly.

Original language	English
Article number	2
Pages (from-to)	1-11
Journal	Australian Journal of Mathematical Analysis and Applications
Volume	13
Issue number	1
Publication status	Published - 2016

Keywords

Hausdorff-Young inequality
42B10 (46B20, 46E40)

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title = "On the Constant in a Transference Inequality for the Vector-valued Fourier Transform",

abstract = "The standard proof of the equivalence of Fourier type on Rd and on the torus Td is usually stated in terms of an implicit constant, defined as the minimum of a sum of powers of sinc functions. In this note we compute this minimum explicitly.",

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author = "Dion Gijswijt and {van Neerven}, Jan",

year = "2016",

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journal = "Australian Journal of Mathematical Analysis and Applications",

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AB - The standard proof of the equivalence of Fourier type on Rd and on the torus Td is usually stated in terms of an implicit constant, defined as the minimum of a sum of powers of sinc functions. In this note we compute this minimum explicitly.

KW - Hausdorff-Young inequality

KW - 42B10 (46B20, 46E40)

M3 - Article

SN - 1449-5910

VL - 13

SP - 1

EP - 11

JO - Australian Journal of Mathematical Analysis and Applications

JF - Australian Journal of Mathematical Analysis and Applications

IS - 1

M1 - 2

ER -

On the Constant in a Transference Inequality for the Vector-valued Fourier Transform

Abstract

Keywords

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