Abstract
It is known that in the case of the unit disk the invertibility of the orthogonal projection of one subspace of H2 which is co-invariant with respect to the shift operator onto another such subspace is connected with the Helson-Szegö theorem and the Muckenhoupt condition. In the present paper, we consider the same problem in character-automorphic Hardy spaces on a finitely connected planar domain. The problem is reduced to estimating the angles between certain subspaces of the weighted L2-space on the boundary of the domain. The answer is given in terms of the Muckenhoupt condition for certain weights. Bibliography: 29 titles.
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Dedicated to the 90th anniversary of G. M. Goluzin's birth
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 237, 1997, pp. 161–193.
This research was supported by the Marsden Fund, grant 96-UOA-MIS-0098.
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Fedorov, S.I. On the angles between subspaces, the muckenhoupt condition, and projection from one co-invariant subspace onto another in the theory of character-automorphic hardy spaces on a multiply connected domain. J Math Sci 95, 2276–2294 (1999). https://doi.org/10.1007/BF02172472
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DOI: https://doi.org/10.1007/BF02172472