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2010 Carleson inequalities on parabolic Bergman spaces
Masaharu Nishio, Noriaki Suzuki, Masahiro Yamada
Tohoku Math. J. (2) 62(2): 269-286 (2010). DOI: 10.2748/tmj/1277298649


We study Carleson inequalities on parabolic Bergman spaces on the upper half space of the Euclidean space. We say that a positive Borel measure satisfies a $(p,q)$-Carleson inequality if the Carleson inclusion mapping is bounded, that is, $q$-th order parabolic Bergman space is embedded in $p$-th order Lebesgue space with respect to the measure under considering. In a recent paper [6], we estimated the operator norm of the Carleson inclusion mapping for the case $q$ is greater than or equal to $p$. In this paper we deal with the opposite case. When $p$ is greater than $q$, then a measure satisfies a $(p,q)$-Carleson inequality if and only if its averaging function is $\sigma$-th integrable, where $\sigma$ is the exponent conjugate to $p/q$. An application to Toeplitz operators is also included.


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Masaharu Nishio. Noriaki Suzuki. Masahiro Yamada. "Carleson inequalities on parabolic Bergman spaces." Tohoku Math. J. (2) 62 (2) 269 - 286, 2010.


Published: 2010
First available in Project Euclid: 23 June 2010

zbMATH: 1204.35013
MathSciNet: MR2663457
Digital Object Identifier: 10.2748/tmj/1277298649

Primary: 35K05
Secondary: 26D10, 31B10

Rights: Copyright © 2010 Tohoku University


Vol.62 • No. 2 • 2010
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