Vol. 62, No. 2, 1976

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Isomorphisms between harmonic and P-harmonic Hardy spaces on Riemann surfaces

Joel Linn Schiff

Vol. 62 (1976), No. 2, 551–560

In this paper we investigate the relationship between the Hardy space Hq(R) of harmonic functions on a hyperbolic Riemann surface R, and the Hardy space Pq(R) of solutions of the equation Δu = Pu, where P 0, P0 is a C1-density on R. Under certain conditions these spaces are shown to be canonically isomorphic, although in general this is not the case. However, specific subspaces are found which are isomorphic and their relationship with other function spaces is discussed.

Mathematical Subject Classification 2000
Primary: 31C05
Received: 29 September 1975
Published: 1 February 1976
Joel Linn Schiff