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Abstract
It is known that if q is an even integer, then the L-q(R-d) 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 statements involving solutions to heat equations. Such considerations are natural given the celebrated theorem of Beckner concerning the gaussian extremisability of the Hausdorff-Young inequality.
Original language | English |
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Pages (from-to) | 971-979 |
Number of pages | 9 |
Journal | Bulletin of the London Mathematical Society |
Volume | 41 |
DOIs | |
Publication status | Published - 3 Sept 2009 |
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Dive into the research topics of 'Heat-flow monotonicity related to the Hausdorff-Young inequality'. Together they form a unique fingerprint.Projects
- 1 Finished
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New Approaches to Central Problems in Euclidean Harmonic Analysis and Geometric Combinatorics
Engineering & Physical Science Research Council
3/01/07 → 2/01/10
Project: Research Councils