scholarly journals Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope

2019 ◽  
Author(s):  
Luigi Ambrosio ◽  
Maria Colombo ◽  
Simone Di Marino
Keyword(s):  
Sobolev Spaces ◽  
Lower Semicontinuity ◽  
Metric Measure Spaces ◽  
Measure 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.

scholarly journals Musielak-Orlicz-Sobolev spaces on metric measure spaces

2015 ◽  
Vol 65 (2) ◽  
pp. 435-474 ◽  
Author(s):  
Takao Ohno ◽  
Tetsu Shimomura
Keyword(s):  
Sobolev Spaces ◽  
Metric Measure Spaces ◽  
Measure Spaces

scholarly journals Morrey-Sobolev Spaces on Metric Measure Spaces

2013 ◽  
Vol 41 (1) ◽  
pp. 215-243 ◽  
Author(s):  
Yufeng Lu ◽  
Dachun Yang ◽  
Wen Yuan
Keyword(s):  
Sobolev Spaces ◽  
Metric Measure Spaces ◽  
Measure Spaces
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