Journal of the Mathematical Society of Japan

Norm estimation of the harmonic Bergman projection on half-spaces

Hyungwoon KOO, Kyesook NAM, and HeungSu YI

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Abstract

On the setting of the upper half-space $\boldsymbol{H}$ of the Euclidean $n$-spaces, we give a sharp norm esitame of the weighted harmonic Bergman projection on $L_\alpha^p$ for $1 < p < \infty$. Also, we obtain the norm estimate of the projection depending on $\alpha > -1$ when p is fixed.

Article information

Source
J. Math. Soc. Japan Volume 61, Number 1 (2009), 225-235.

Dates
First available in Project Euclid: 9 February 2009

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1234189034

Digital Object Identifier
doi:10.2969/jmsj/06110225

Mathematical Reviews number (MathSciNet)
MR2272877

Zentralblatt MATH identifier
05530297

Subjects
Primary: 31B05: Harmonic, subharmonic, superharmonic functions
Secondary: 31B10: Integral representations, integral operators, integral equations methods 30D45: Bloch functions, normal functions, normal families 30D55

Keywords
weighted Bergman kernel harmonic Bergman functions Bergman projection upper half-space

Citation

KOO, Hyungwoon; NAM, Kyesook; YI, HeungSu. Norm estimation of the harmonic Bergman projection on half-spaces. J. Math. Soc. Japan 61 (2009), no. 1, 225--235. doi:10.2969/jmsj/06110225. http://projecteuclid.org/euclid.jmsj/1234189034.


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References

  • H. Koo, K. Nam and H. Yi, Weighted harmonic Bergman kernel on half-spaces, J. Math. Soc. Japan, 58 (2006), 351–362.
  • H. Koo, K. Nam and H. Yi, Weighted harmonic Bergman functions on half-spaces, J. Korean Math. Soc., 42 (2005), 975–1002.
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  • K. Zhu, A sharp norm estimate of the Bergman projection on $L^p$ spaces, Contemporary Mathematics, 404 (2006), 199–205.