Source: Tohoku Math. J. (2) Volume 62, Number 2
(2010), 269-286.
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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References
B. R. Choe and H. Yi, Representations and interpolations of harmonic Bergman functions on half-spaces, Nagoya Math. J. 151 (1998), 51--89.
B. R. Choe, H. Koo and H. Yi, Positive Toeplitz operators between the harmonic Bergman spaces, Potential Anal. 17 (2002), 307--335.
D. Luecking, Multipliers of Bergman spaces into Lebesgue spaces, Proc. Edinburgh Math. Soc. (2) 29 (1986), 125--131.
Mathematical Reviews (MathSciNet):
MR829188
M. Nishio, K. Shimomura and N. Suzuki, $\alpha$-parabolic Bergman spaces, Osaka J. Math. 42 (2005), 133--162.
M. Nishio K. Shimomura and N. Suzuki, $L^p$-boundedness of Bergman projections for $\alpha$-parabolic operators, Potential theory in Matsue, 305--318, Adv. Stud. Pure Math. 44, Math. Soc. Japan, Tokyo, 2006.
M. Nishio, N. Suzuki and M. Yamada, Toeplitz operators and Carleson measures on parabolic Bergman spaces, Hokkaido Math. J. 36 (2007), 563--583.
M. Nishio, N. Suzuki and M. Yamada, Compact Toeplitz operators on parabolic Bergman spaces, Hiroshima Math. J. 38 (2008), 177--192.
M. Nishio, N. Suzuki and M. Yamada, Interpolating sequences of parabolic Bergman spaces, Potential Anal. 28 (2008), 357--378.
M. Nishio, N. Suzuki and M. Yamada, Weighted Berezin transformations with application to Toeplitz operators of Schatten class on the parabolic Bergman spaces, Kodai Math. J. 32 (2009), 501--520.
M. Nishio and M. Yamada, Carleson type measures on parabolic Bergman spaces, J. Math. Soc. Japan 58 (2006), 83--96.
W. Ramey and H. Yi, Harmonic Bergman functions on half-spaces, Trans. Amer. Math. Soc. 348 (1996), 633--660.
