Geodesic
On the angles between subspaces, Muckenhoupt condition,
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 14, Tome 237 (1997), pp. 161-193 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is known that in the case of the unit disk the invertibility of the orthogonal projection of one subspace of $H_2$ which is co-invariant with respect to the shift operator onto another such subspace is connected with the Helson–Szegő 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 $L_2$-space on the boundary of the domain. The answer is given in terms of the Muckenhoupt condition for certain weights. 
@article{ZNSL_1997_237_a12,
     author = {S. I. Fedorov},
     title = {On the angles between subspaces, {Muckenhoupt} condition,},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {161--193},
     year = {1997},
     volume = {237},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_237_a12/}
}
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S. I. Fedorov. On the angles between subspaces, Muckenhoupt condition,. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 14, Tome 237 (1997), pp. 161-193. http://geodesic.mathdoc.fr/item/ZNSL_1997_237_a12/