scholarly journals A sharp subelliptic Sobolev embedding theorem with weights

2015 ◽  
Vol 47 (3) ◽  
pp. 396-406 ◽  
Author(s):  
Po-Lam Yung
Keyword(s):  
Embedding Theorem ◽  
Sobolev Embedding ◽  
Sobolev Embedding Theorem

scholarly journals A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin–Triebel spaces with mixed norms

2007 ◽  
Vol 5 (2) ◽  
pp. 183-198 ◽  
Author(s):  
Jon Johnsen ◽  
Winfried Sickel
Keyword(s):  
Sobolev Spaces ◽  
Direct Proof ◽  
Embedding Theorem ◽  
Sobolev Embedding ◽  
Homogeneous Type ◽  
Sobolev Embedding Theorem ◽  
Mixed Norms ◽  
Sobolev Embeddings ◽  
Special Cases ◽  
Anisotropic Spaces

The article deals with a simplified proof of the Sobolev embedding theorem for Lizorkin–Triebel spaces (that contain theLp-Sobolev spacesHpsas special cases). The method extends to a proof of the corresponding fact for general Lizorkin–Triebel spaces based on mixedLp-norms. In this context a Nikol' skij–Plancherel–Polya inequality for sequences of functions satisfying a geometric rectangle condition is proved. The results extend also to anisotropic spaces of the quasi-homogeneous type.

scholarly journals Heat Kernel Estimates Under the Ricci–Harmonic Map Flow

2017 ◽  
Vol 60 (4) ◽  
pp. 831-857 ◽  
Author(s):  
Mihai Băileşteanu ◽  
Hung Tran
Keyword(s):  
Ricci Flow ◽  
Harmonic Map ◽  
Embedding Theorem ◽  
Sobolev Embedding ◽  
Sobolev Embedding Theorem ◽  
Kernel Estimates ◽  
Best Constant ◽  
Entropy Functional ◽  
Conjugate Heat Equation ◽  
Harmonic Map Flow

AbstractThis paper considers the Ricci flow coupled with the harmonic map flow between two manifolds. We derive estimates for the fundamental solution of the corresponding conjugate heat equation and we prove an analogue of Perelman's differential Harnack inequality. As an application, we find a connection between the entropy functional and the best constant in the Sobolev embedding theorem in ℝn.

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