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Banach spaces of bounded solutions of Δu = Pu (P ≥ 0) on hyperbolic riemann surfaces

Published online by Cambridge University Press:  22 January 2016

Mitsuru Nakai
Mitsuru Nakai*
Affiliation:
Nagoya University
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Consider a nonnegative Hölder continuous 2-form P(z)dxdy on a hyperbolic Riemann surface R (z = x + iy). We denote by PB(R) the Banach space of solutions of the equation Δu = Pu on R with finite supremum norms. We are interested in the question how the Banach space structure of PB(R) depends on P. Precisely we consider two such 2-forms P and Q on R and compare PB(R) and QB(R). If there exists a bijective linear isometry T of PB(R) to QB(R), then we say that PB(R) and QB(R) are isomorphic.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 53 , May 1974 , pp. 141 - 155
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1974

References

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