• Corpus ID: 239769117

Fundamental properties of Cauchy--Szeg\H{o} projection on quaternionic Siegel upper half space and applications

@inproceedings{Chang2021FundamentalPO,
  title={Fundamental properties of Cauchy--Szeg\H\{o\} projection on quaternionic Siegel upper half space and applications},
  author={Der-Chen Chang and Xuan Thinh Duong and Ji Li and Wei Wang and Qingyan Wu},
  year={2021}
}
We investigate the Cauchy–Szegő projection for quaternionic Siegel upper half space to obtain the pointwise (higher order) regularity estimates for Cauchy–Szegő kernel and prove that the Cauchy– Szegő kernel is non-zero everywhere, which further yields a non-degenerated pointwise lower bound. As applications, we prove the uniform boundedness of Cauchy–Szegő projection on every atom on the quaternionic Heisenberg group, which is used to give an atomic decomposition of regular Hardy space H on… 

References

SHOWING 1-10 OF 68 REFERENCES
An explicit formula of Cauchy-Szego kernel for quaternionic Siegel upper half space and applications
In this paper we obtain an explicit formula of Cauchy--Szeg\"{o} kernel for quaternionic Siegel upper half space, and then based on this, we prove that the Cauchy--Szeg\"{o} projection on
On the Cauchy–Szegö Kernel for Quaternion Siegel Upper Half-Space
The work is dedicated to the construction of the Cauchy–Szegö kernel for the Cauchy–Szegö projection integral operator from the space of $$L^2$$-integrable functions defined on the boundary of the
The k-Cauchy–Fueter complex, Penrose transformation and Hartogs phenomenon for quaternionic k-regular functions
Abstract By using complex geometric method associated to the Penrose transformation, we give a complete derivation of an exact sequence over C 4 n , whose associated differential complex over H n is
The tangential k-Cauchy–Fueter complexes and Hartogs’ phenomenon over the right quaternionic Heisenberg group
  • Yun Shi, W. Wang
  • Mathematics
    Annali di Matematica Pura ed Applicata (1923 -)
  • 2019
We construct the tangential $k$-Cauchy-Fueter complexes on the right quaternionic Heisenberg group, as the quaternionic counterpart of $\overline{\partial}_b$-complex on the Heisenberg group in the
Subadditivity of homogeneous norms on certain nilpotent Lie groups
Let N be a Lie group with its Lie algebra generated by the leftinvariant vector fields Xi,.. . ,Xk on N. An explicit fundamental solution for the (hypoelliptic) operator L = Xx + ■ ■ ■ + Xk on N has
On the quaternionic Monge-Ampere operator, closed positive currents and Lelong-Jensen type formula on the quaternionic space
Abstract In this paper, we introduce the first-order differential operators d 0 and d 1 acting on the quaternionic version of differential forms on the flat quaternionic space H n . The behavior of d
Regular functions of several quaternionic variables and the Cauchy-Fueter complex
We employ a classical idea of Ehrenpreis, together with a new algebraic result, to give a new proof that regular functions of several quaternionic variables cannot have compact singularities. As a
Invariant resolutions for several Fueter operators
Abstract A proper generalization of complex function theory to higher dimension is Clifford analysis and an analogue of holomorphic functions of several complex variables were recently described as
Nearly weakly orthonormal sequences, singular value estimates, and Calderon-Zygmund operators
Abstract The direct way to estimate the singular values of a compact operator is to decompose it as a sum of orthogonal rank one pieces. However, such decompositions can generally not be found in
Stratified Lie groups and potential theory for their sub-Laplacians
The existence, for every sub-Laplacian, of a homogeneous fundamental solution smooth out of the origin, plays a crucial role in the book. This makes it possible to develop an exhaustive Potential
...
1
2
3
4
5
...