Geodesic
Lp Behavior of the Eigenfunctions of the Invariant Laplacian
Canadian mathematical bulletin, Tome 36 (1993) no. 4, pp. 458-465

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Let 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 X 0, 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 ≥ 1⁄2 and λ = 4n 2 α(α — 1), we obtain a necessary and sufficient condition for a function f in Xλ to be represented as for some F ∊ LP (∂B).
DOI : 10.4153/CMB-1993-061-2
Mots-clés : 31B10, 31B35, Invariant Laplacian 
Kwon, E. G. Lp Behavior of the Eigenfunctions of the Invariant Laplacian. Canadian mathematical bulletin, Tome 36 (1993) no. 4, pp. 458-465. doi: 10.4153/CMB-1993-061-2
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     title = {Lp {Behavior} of the {Eigenfunctions} of the {Invariant} {Laplacian}},
     journal = {Canadian mathematical bulletin},
     pages = {458--465},
     year = {1993},
     volume = {36},
     number = {4},
     doi = {10.4153/CMB-1993-061-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-061-2/}
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