Fractional Laplacian, homogeneous Sobolev spaces and their realizations
نویسندگان
چکیده
منابع مشابه
Composition in Fractional Sobolev Spaces
1. Introduction. A classical result about composition in Sobolev spaces asserts that if u ∈ W k,p (Ω)∩L ∞ (Ω) and Φ ∈ C k (R), then Φ • u ∈ W k,p (Ω). Here Ω denotes a smooth bounded domain in R N , k ≥ 1 is an integer and 1 ≤ p < ∞. This result was first proved in [13] with the help of the Gagliardo-Nirenberg inequality [14]. In particular if u ∈ W k,p (Ω) with kp > N and Φ ∈ C k (R) then Φ • ...
متن کاملThe Laplacian on homogeneous spaces
The solution of the eigenvalue problem of the Laplacian on a general homogeneous space G/H is given. Here G is a compact, semi-simple Lie group, H is a closed subgroup of G, and the rank of H is equal to the rank of G. It is shown that the multiplicity of the lowest eigenvalue of the Laplacian on G/H is just the degeneracy of the lowest Landau level for a particle moving on G/H in the presence ...
متن کاملThe Poisson equation in homogeneous Sobolev spaces
We consider Poisson’s equation in an n-dimensional exterior domain G (n≥ 2) with a sufficiently smooth boundary. We prove that for external forces and boundary values given in certain Lq(G)-spaces there exists a solution in the homogeneous Sobolev space S2,q(G), containing functions being local in Lq(G) and having second-order derivatives in Lq(G). Concerning the uniqueness of this solution we ...
متن کاملFock-sobolev Spaces and Their Carleson Measures
We consider the Fock-Sobolev space F p,m consisting of entire functions f such that f , the m-th order derivative of f , is in the Fock space F . We show that an entire function f is in F p,m if and only if the function zf(z) is in F . We also characterize the Carleson measures for the spaces F , establish the boundedness of the weighted Fock projection on appropriate L spaces, identify the Ban...
متن کاملFrames and Homogeneous Spaces
Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annali di Matematica Pura ed Applicata (1923 -)
سال: 2020
ISSN: 0373-3114,1618-1891
DOI: 10.1007/s10231-020-00966-7