Positive Gaussian Kernels Also Have Gaussian Minimizers
Book Details
Format
Paperback / Softback
Book Series
Memoirs of the American Mathematical Society
ISBN-10
1470451433
ISBN-13
9781470451431
Publisher
American Mathematical Society
Imprint
American Mathematical Society
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jun 30th, 2022
Print length
90 Pages
Weight
194 grams
Product Classification:
Probability & statisticsProbability and statistics
Ksh 13,150.00
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Examines lower bounds on multilinear operators with Gaussian kernels acting on Lebesgue spaces, with exponents below one. The authors put forward natural conditions when the optimal constant can be computed by inspecting centered Gaussian functions only, and we give necessary and sufficient conditions for this constant to be positive.
We study lower bounds on multilinear operators with Gaussian kernels acting on Lebesgue spaces, with exponents below one. We put forward natural conditions when the optimal constant can be computed by inspecting centered Gaussian functions only, and wegive necessary and sufficient conditions for this constant to be positive. Our work provides a counterpart to Lieb''s results on maximizers of multilinear operators with real Gaussian kernels, also known as the multidimensional Brascamp-Lieb inequality. It unifies and extends severalinverse inequalities.
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