Hitchhiker's guide to the fractional Sobolev spaces. Di Nezza, E., Palatucci, G., & Valdinoci, E. Bulletin des Sciences Mathématiques, 136(5):521–573, 2012.
doi  bibtex   
@Article{         Di-Nezza_2012aa,
  author        = {Di Nezza, E. and Palatucci, G. and Valdinoci, E.},
  doi           = {10.1016/j.bulsci.2011.12.004},
  group         = {wolf},
  journal       = {Bulletin des Sciences Mathématiques},
  langid        = {english},
  number        = {5},
  pages         = {521--573},
  title         = {Hitchhiker's guide to the fractional {Sobolev} spaces},
  volume        = {136},
  year          = {2012}
}

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