Commutators of Lipschitz Functions and Singular Integrals with Non-Smooth Kernels on Euclidean Spaces

2016 ◽  
Vol 32 (2) ◽  
pp. 135-148
Author(s):  
H. V. Le
Keyword(s):  
Singular Integrals ◽  
Lipschitz Functions ◽  
Euclidean Spaces ◽  
Smooth Kernels

scholarly journals Characterisation of upper gradients on the weighted Euclidean space and applications

2021 ◽  
Author(s):  
Danka Lučić ◽  
Enrico Pasqualetto ◽  
Tapio Rajala
Keyword(s):  
Euclidean Space ◽  
Sobolev Space ◽  
Radon Measure ◽  
Lipschitz Functions ◽  
Euclidean Spaces ◽  
Upper Gradient

AbstractIn the context of Euclidean spaces equipped with an arbitrary Radon measure, we prove the equivalence among several different notions of Sobolev space present in the literature and we characterise the minimal weak upper gradient of all Lipschitz functions.

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