Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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WEIGHTED HARMONIC BERGMAN FUNCTIONS ON HALF-SPACES

  • Published : 2005.09.01
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Abstract

On the setting of the upper half-space H of the Eu­clidean n-space, we show the boundedness of weighted Bergman projection for 1 < p < $\infty$ and nonorthogonal projections for 1 $\leq$ p < $\infty$ . Using these results, we show that Bergman norm is equiva­ lent to the normal derivative norms on weighted harmonic Bergman spaces. Finally, we find the dual of b$\_{$^{1}$.

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References

  1. S. Axler, P. Bourdon, and W. Ramey, Harmonic function theory, Springer-Verlag, New York, 1992
  2. F. Beatrous, Behavior of holomorphic functions near weakly pseudoconvex boundary points, Indiana Univ. Math. J. 40 (1991), no. 3, 915-966 https://doi.org/10.1512/iumj.1991.40.40041
  3. B. R. Choe, Projections, the weighted Bergman spaces, and the Bloch space, Proc. Amer. Math. Soc. 108 (1990), 127-136
  4. B. R. Choe, H. Koo, and H. Yi, Bergman norm estimates of Poisson integrals, Nagoya Math. J. 161 (2001), 85-125 https://doi.org/10.1017/S0027763000022145
  5. B. R. Choe, H. Koo, and H. Yi, Moment vanishing properties of harmonic Bergman functions, preprint
  6. R. R. Coifman and R. Rochberg, Representation theorems for holomorphic and harmonic functions in $L^P$, Asterisque 77 (1980), 11-66
  7. H. Kang and H. Koo, Estimates of the harmonic Bergman kernel on smooth domains, J. Funct. Anal. 185 (2001), 220-239 https://doi.org/10.1006/jfan.2001.3761
  8. H. Koo, K. Nam, and H. Yi, Weighted harmonic Bergman kernel on Half-spaces, to appear J. Math. Soc. Japan
  9. H. Hedenmalm, B. Korenblum, and K. Zhu, Theory of Bergman spaces, Springer-Verlag, New York, 2000
  10. W. Ramey and H. Yi, Harmonic Bergman functions on half-spaces, Trans. Amer. Math. Soc. 348 (1996), 633-660 https://doi.org/10.1090/S0002-9947-96-01383-9

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