Geodesic
Functions Belonging to a Dirichlet Subalgebra of the Disk Algebra
Canadian mathematical bulletin, Tome 18 (1975) no. 3, pp. 375-377

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Browder and Wermer in [2] give a method for constructing Dirichlet subalgebras of the disk algebra. In this note we show that these Dirichlet algebras do not contain any non-constant functions which satisfy a Lipschitz-one condition on a subinterval of the unit circle. 
Lund, Bruce. Functions Belonging to a Dirichlet Subalgebra of the Disk Algebra. Canadian mathematical bulletin, Tome 18 (1975) no. 3, pp. 375-377. doi: 10.4153/CMB-1975-068-5
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     title = {Functions {Belonging} to a {Dirichlet} {Subalgebra} of the {Disk} {Algebra}},
     journal = {Canadian mathematical bulletin},
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     year = {1975},
     volume = {18},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-068-5/}
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