On Sharp Constants for Dual Segal--Bargmann L^p Spaces

2014/01/09 by William E. Gryc, Gryc, William E., Todd Kemp +1
Mathematics · #32A37 #42B35 #46E15 #47B32 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:32A37 #msc:42B35 #msc:46E15 #msc:47B32

paper · pdf · doi:10.48550/arxiv.1401.1866

arxiv created 2014/08/23 · arxiv updated 2014/08/26

Abstract

We study dilated holomorphic L^p space of Gaussian measures over ℂⁿ, denoted H_p,αⁿ with variance scaling parameter α>0. The duality relations (H_p,αⁿ)^∗ ≅ H_p',α hold with (1)/(p)+(1)/(p')=1, but not isometrically. We identify the sharp lower constant comparing the norms on H_p',α and (H_p,αⁿ)^∗, and provide upper and lower bounds on the sharp upper constant. We prove several suggestive partial results on the sharpness of the upper constant. One of these partial results leads to a sharp bound on each Taylor coefficient of a function in the Fock space for n=1.

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