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Estimates of fundamental solution for Kohn Laplacian in Besov and Triebel-Lizorkin spaces.
- Source :
- Applicable Analysis; Feb2024, Vol. 103 Issue 4, p763-789, 27p
- Publication Year :
- 2024
-
Abstract
- We introduce Besov space $ \dot {B}_{p}^{\alpha,q}(\partial \Omega _k) $ B ˙ p α , q (∂ Ω k) and Triebel-Lizorkin space $ \dot {F}^{\alpha,q}_{p}(\partial \Omega _k) $ F ˙ p α , q (∂ Ω k) on a family of model domains $ \partial \Omega _k=\left \{(\mathbf{z},z_{n+1})=(z_1,z_2,\ldots, z_{n+1}):\right. \left. \mbox {Im} (z_{n+1})=\phi (|\mathbf{z}|^2)\right \} $ ∂ Ω k = { (z , z n + 1) = (z 1 , z 2 , ... , z n + 1) : Im (z n + 1) = ϕ (| z | 2) } with $ \phi (x)=x^{k} $ ϕ (x) = x k in $ \mathbf {C}^{n+1} $ C n + 1 which can be considered as a space of homogeneous type in the sense of Coifman RR, Weiss G.[Analyse Harmonique Non-commutative and Certains Espaces Homogǹes. Berlin: Springer; 1971. (Lecture Notes in Math.; 242).], Coifman R, Weiss G. [Extensions of Hardy spaces and their use in analysis. Bull Amer Math Soc. 1977;83:569–645.]. We study the sharp estimates on the fundamental solution for the Kohn Laplacian and Cauchy-Szegö projection on $ \partial \Omega _k $ ∂ Ω k in these spaces. [ABSTRACT FROM AUTHOR]
- Subjects :
- BESOV spaces
HOMOGENEOUS spaces
MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00036811
- Volume :
- 103
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Applicable Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 175301452
- Full Text :
- https://doi.org/10.1080/00036811.2023.2208752