# 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

- MathematicsIndiana University Mathematics Journal
- 2021

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

- Mathematics
- 2013

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

- Mathematics
- 2010

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

- MathematicsAnnali 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

- Mathematics
- 1981

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

- Mathematics
- 2017

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

- Mathematics
- 1999

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

- Mathematics
- 2006

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

- Mathematics
- 1989

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

- Mathematics
- 2007

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…