Geodesic
Criteria of the removable sets for the weighted spaces of garmonic functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 18, Tome 286 (2002), pp. 62-73

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Sharp functional, capacity, and metric characteristics of removable sets for harmonic functions without fluxions in the weighted space $L^1_{p,\omega}$ with the Muckenhoupt weight are found. 
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     author = {I. N. Demshin and V. A. Shlyk},
     title = {Criteria of the removable sets for the weighted spaces of garmonic functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     volume = {286},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_286_a4/}
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I. N. Demshin; V. A. Shlyk. Criteria of the removable sets for the weighted spaces of garmonic functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 18, Tome 286 (2002), pp. 62-73. http://geodesic.mathdoc.fr/item/ZNSL_2002_286_a4/