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Abstract
It is known that if q is an even integer, then the Lq(Rd) 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 HausdorffYoung inequality.
Original language  English 

Pages (fromto)  971979 
Number of pages  9 
Journal  Bulletin of the London Mathematical Society 
Volume  41 
DOIs  
Publication status  Published  3 Sep 2009 
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Dive into the research topics of 'Heatflow monotonicity related to the HausdorffYoung inequality'. Together they form a unique fingerprint.Projects
 1 Finished

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