Geodesic
Reproducing kernels and extremal functions in Dirichlet type spaces
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 26, Tome 255 (1998), pp. 198-220

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A number of identities is established for reproducing kernels and extremal functions in Dirichlet type spaces. In certain cases these identities are characteristic. A new proof of Aleman's theorem on extremal functions as contractive multipliers is obtained. As distinct from the original one, it can be extended to vector-valued spaces. 
@article{ZNSL_1998_255_a13,
     author = {S. M. Shimorin},
     title = {Reproducing kernels and extremal functions in {Dirichlet} type spaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {198--220},
     publisher = {mathdoc},
     volume = {255},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_255_a13/}
}
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S. M. Shimorin. Reproducing kernels and extremal functions in Dirichlet type spaces. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 26, Tome 255 (1998), pp. 198-220. http://geodesic.mathdoc.fr/item/ZNSL_1998_255_a13/