The LBB condition in fractional Sobolev spaces and applications

2008 ◽  
Vol 29 (3) ◽  
pp. 790-805 ◽  
Author(s):  
J.-L. Guermond
Keyword(s):  
Sobolev Spaces ◽  
Fractional Sobolev Spaces ◽  
Lbb Condition

scholarly journals Composition in fractional Sobolev spaces

2001 ◽  
Vol 7 (2) ◽  
pp. 241-246 ◽  
Author(s):  
Haim Brezis ◽  
◽  
Petru Mironescu ◽  
Keyword(s):  
Sobolev Spaces ◽  
Fractional Sobolev Spaces

A density result for fractional Sobolev spaces

2016 ◽  
pp. 43-62
Author(s):  
Giovanni Molica Bisci ◽  
Vicentiu D. Radulescu ◽  
Raffaella Servadei
Keyword(s):  
Sobolev Spaces ◽  
Fractional Sobolev Spaces ◽  
Density Result

scholarly journals Local maximal operators on fractional Sobolev spaces

2016 ◽  
Vol 68 (3) ◽  
pp. 1357-1368 ◽  
Author(s):  
Hannes LUIRO ◽  
Antti V. VÄHÄKANGAS
Keyword(s):  
Sobolev Spaces ◽  
Maximal Operators ◽  
Fractional Sobolev Spaces

Generalized Littlewood–Paley characterizations of fractional Sobolev spaces

2018 ◽  
Vol 20 (07) ◽  
pp. 1750077 ◽  
Author(s):  
Shuichi Sato ◽  
Fan Wang ◽  
Dachun Yang ◽  
Wen Yuan
Keyword(s):  
Sobolev Spaces ◽  
Weak Type ◽  
Metric Measure Spaces ◽  
Fractional Sobolev Spaces ◽  
Area Function ◽  
Weak Type Estimates ◽  
Measure Spaces ◽  
Lusin Area Function

In this paper, the authors characterize the Sobolev spaces [Formula: see text] with [Formula: see text] and [Formula: see text] via a generalized Lusin area function and its corresponding Littlewood–Paley [Formula: see text]-function. The range [Formula: see text] is also proved to be nearly sharp in the sense that these new characterizations are not true when [Formula: see text] and [Formula: see text]. Moreover, in the endpoint case [Formula: see text], the authors also obtain some weak type estimates. Since these generalized Littlewood–Paley functions are of wide generality, these results provide some new choices for introducing the notions of fractional Sobolev spaces on metric measure spaces.

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