Journal of Mathematical Sciences

, Volume 166, Issue 3, pp 357–376 | Cite as

Fractional Sobolev, Moser–Trudinger, Morrey–Sobolev inequalities under Lorentz norms


We consider the Sobolev type inequalities under Lorentz norms on bounded open domains for fractional derivatives (−∆)s/2 in the following three cases: n > ps, n = ps, and n < ps, whence establishing the weak type Sobolev inequalities, Moser–Trudinger and Morrey–Sobolev inequalities for fractional derivatives in Lorentz norms. Applying these inequalities, we obtain the trace forms of six related functional inequalities. Bibliography: 44 titles.


Fractional Derivative Sobolev Inequality Open Domain Lorentz Space Logarithmic Sobolev Inequality 
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© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.Memorial University of NewfoundlandSt. John’sCanada
  2. 2.University of AlbertaAlbertaCanada

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