Geodesic
Null-sets criteria for weighed Sobolev spaces
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 17, Tome 276 (2001), pp. 52-82 
I. N. Demshin; Yu. V. Dymchenko; V. A. Shlyk. Null-sets criteria for weighed Sobolev spaces. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 17, Tome 276 (2001), pp. 52-82. http://geodesic.mathdoc.fr/item/ZNSL_2001_276_a3/
@article{ZNSL_2001_276_a3,
     author = {I. N. Demshin and Yu. V. Dymchenko and V. A. Shlyk},
     title = {Null-sets criteria for weighed {Sobolev} spaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {52--82},
     year = {2001},
     volume = {276},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_276_a3/}
}
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We establish exact functional, capacity, and metric characteristics for null-sets in weighted Sobolev spaces with the Muckenhoupt weight.