Lp Behavior of the Eigenfunctions of the Invariant Laplacian
Keyword(s):
AbstractLet be the invariant Laplacian on the open unit ball B of Cn and let Xλ denote the set of those f € C2(B) such that counterparts of some known results on X0, i.e. on M-harmonic functions, are investigated here. We distinguish those complex numbers λ for which the real parts of functions in Xλ belongs to Xλ. We distinguish those λ for which the Maximum Modulus Priniple remains true. A kind of weighted Maximum Modulus Principle is presented. As an application, setting α ≥ ½ and λ = 4n2α(α — 1), we obtain a necessary and sufficient condition for a function f in Xλ to be represented asfor some F ∊ LP(∂B).
1978 ◽
Vol 30
(01)
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pp. 22-31
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1990 ◽
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pp. 180-192
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1990 ◽
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1979 ◽
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pp. 255-263
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1978 ◽
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pp. 31-45
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1972 ◽
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1981 ◽
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pp. 25-50
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1996 ◽
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pp. 275-283
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1963 ◽
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pp. 267-273
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1982 ◽
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pp. 718-736
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