Harmonic functions on finitely sheeted unlimited covering surfaces

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概要

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• We denote by HP(R) and (HB(R), resp.) the class of positive (bounded, resp.) harmonic functions on a Riemann surface R. Consider an open Riemann surface W possessing a Greens function and a p-sheeted ( 1<p<∞) unlimited covering surface ˜{W} of W with projection map \varphi. We give a necessary and sufficient condition, in terms of Martin boundary, for HX(W)\circ\varphi=HX(˜{W})(X=P, B). We also give some examples illustrating the above result when W is the unit disc.

• 社団法人 日本数学会の論文
• 2003-04-01

著者

• Segawa Shigeo

  Department Of Mathematics Daido Institue Of Technology

• Segawa Shigeo

  Department Of Mathematics Daido Institute Of Technology

• Masaoka Hiroaki

  Department Of Mathematics Faculty Of Science

関連論文

• P-harmonic dimensions on ends
• Harmonic functions on finitely sheeted unlimited covering surfaces
• Harmonic dimension of covering surfaces : dedicated to Professor Mitsuru Nakai on his sixtieth birthday
• Examples of harmonic Hardy-Orlicz spaces on the plane with finitely many punctures (Potential Theory and its Related Fields)

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