MINIMIZERS FOR THE EMBEDDING OF BESOV SPACES

Mingjuan Chen

doi:10.11948/2017100

2017 Volume 7 Issue 4

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Mingjuan Chen. MINIMIZERS FOR THE EMBEDDING OF BESOV SPACES[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1637-1651. doi: 10.11948/2017100

Citation:

Mingjuan Chen. MINIMIZERS FOR THE EMBEDDING OF BESOV SPACES[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1637-1651. doi: 10.11948/2017100

MINIMIZERS FOR THE EMBEDDING OF BESOV SPACES

Mingjuan Chen

School of Mathematical Sciences, Peking University, Beijing, 100871, China

Abstract

Abstract

Using the profile decomposition, we will show the relatively compactness of the minimizing sequence to the critical embeddings between Besov spaces, which implies the existence of minimizer of the critical embeddings of Besov spaces Ḃ_p1,q1^s1 ↪ Ḃ_p2,q2^s2 in d dimensions with s₁ -d/p₁=s₂ -d/p₂, s₁>s₂ and 1 ≤ q₁ < q₂ ≤ ∞. Moreover, we establish the nonexistence of the minimizer in the case Ḃ_p1,q^s1 ↪ Ḃ_p2,q^s2.
- Profile decomposition /
- Besov embedding /
- minimizer /
- compactness
MSC: 46E35;46B50

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References

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