Abstract
On the setting of the half-spaceR n−1×R +, we investigate Gleason's problem for harmonic Bergman and Bloch functions. We prove that Gleason's problem for the harmonicL p-Bergman space is solvable if and only ifp>n. We also prove that Gleason's problem for the harmonic (little) Bloch space is solvable.
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References
S. Axler, P. Bourdon and W. Ramey,Harmonic function theory, Springer-Verlag, New York, 1992.
B. R. Choe,Projections, the weighted Bergman spaces, and the Bloch space, Proc. Amer. Math. Soc. 108(1990), 127–136.
B. R. Choe, H. Koo, and H. Yi,Bergman norm estimates of Poisson integrals, preprint.
F. Forelli and W. Rudin,Projections on spaces of holomorphic functions in balls, Indiana Univ. Math. J.24 (1974), 593–602.
A. M. Gleason,Finitely generated ideals in Banach spaces, J. Math. and Mechanics 13(1964), 125–132.
W. Ramey and H. Yi,Harmonic Bergman functions on half-spaces, Trans. Amer. Math. Soc.348(1996), 633–660.
W. Rudin,Function theory in the unit ball of C n, Springer-Verlag, New York, 1980
A. Shields and D. Williams,Bounded projections, duality, and multipliers in space of analytic functions, Trans. Amer. Math. Soc.162 (1971), 287–302.
H. Yi,Harmonic little Bloch functions on half-spaces, Math. Japonica.47(1998), 21–28.
K. Zhu,The Bergman spaces, the Bloch space and Gleason's problem, Trans. Amer. Math. Soc. 309(1988), 253–268.
K. Zhu,Operator theory in function spaces, Marcel Dekker, New York and Basel, 1990.
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Choe, B.R., Koo, H. & Yi, H. Gleason's problem for harmonic Bergman and Bloch functions on half-spaces. Integr equ oper theory 36, 269–287 (2000). https://doi.org/10.1007/BF01213925
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DOI: https://doi.org/10.1007/BF01213925