Szeg\"{o} projections for Hardy spaces in quaternionic Clifford analysis
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In this paper we study Szeg\"{o} kernel projections for Hardy spaces in quaternionic Clifford analysis. At first we introduce the matrix Szeg\"{o} projection operator for the Hardy space of quaternionic Hermitean monogenic functions by the characterization of the matrix Hilbert transform in the quaternionic Clifford analysis. Then we establish the Kerzman-Stein formula which closely connects the matrix Szeg\"{o} projection operator with the Hardy projection operator onto the Hardy space, and we get the matrix Szeg\"{o} projection operator in terms of the Hardy projection operator and its adjoint. At last, we construct the explicit matrix Szeg\"o kernel function for the Hardy space on the sphere as an example, and get the solution to a Diriclet boundary value problem for matrix functions.
Abstract
In this paper we study Szeg\"{o} kernel projections for Hardy spaces in quaternionic Clifford analysis. At first we introduce the matrix Szeg\"{o} projection operator for the Hardy space of quaternionic Hermitean monogenic functions by the characterization of the matrix Hilbert transform in the quaternionic Clifford analysis. Then we establish the Kerzman-Stein formula which closely connects the matrix Szeg\"{o} projection operator with the Hardy projection operator onto the Hardy space, and we get the matrix Szeg\"{o} projection operator in terms of the Hardy projection operator and its adjoint. At last, we construct the explicit matrix Szeg\"o kernel function for the Hardy space on the sphere as an example, and get the solution to a Diriclet boundary value problem for matrix functions.
참고문헌 (19)
- R. Abreu-Blaya, "Boundary value problems on fractal hypersurfaces for the quaternionic Hermitian system in R4n", Complex Anal. Oper. Theory, 9(5), pp.957~973 (2015)[DOI]
- R. Abreu-Blaya, "Cauchy integral formulae in quaternionic Hermitean Clifford analysis", Complex Anal. Oper. Theory, 6(5), pp.971~985 (2012)[DOI]
- R. Abreu-Blaya, "Boundary value problems for the quaternionic Hermitian system in R4n", Boundary Value Problems (2012)
- R. Abreu-Blaya, "Matrix Cauchy and Hilbert transforms in Hermitian quaternionic Clifford analysis", Complex Var. Elliptic Equ, 58(8), pp.1057~1069 (2013)[DOI]
- R. Abreu-Blaya, "Polyanalytic Hardy decomposition of higher order Lipschitz functions", J. Math. Anal. Appl, 493(2), pp.10~ (2021)[DOI]
- S. R. Bell, "Solving the Dirichlet problem in the plane by means of the Cauchy integral", Indiana Univ. Math. J, 39(4), pp.1355~1371 (1990)[DOI]
- S. R. Bell, "The Szego projection and the classical objects of potential theory in the plane", Duke Math. J, 64(1), pp.1~26 (1991)[DOI]
- S. Bernstein, "Szeg˝o projections for Hardy spaces of monogenic functions and applications", Int. J. Math. Math. Sci, 29(10), pp.613~624 (2002)[DOI]
- F. Brackx, "Clifford analysis, Research Notes in Mathematics" (1982), Advanced Publishing Program
- D. Constales, "Szegö and Polymonogenic Bergman Kernels for Half-Space and Strip Domains, and Single-Periodic Functions in Clifford Analysis", Complex Variables, Theory and Application: An International Journal, 47(4), pp.349~360 (2002), Informa UK Limited[DOI]
- R. Delanghe, "Clifford algebra and spinor-valued functions", Mathematics and its Applications, 53 (1992), Kluwer Academic Publishers Group[DOI]
- J. E. Gilbert, "Clifford algebras and Dirac operators in harmonic analysis", Cambridge Studies in Advanced Mathematics, 26 (1991), Cambridge University Press[DOI]
- Fuli HE, "Szegö kernel for hardy space of matrix functions", Acta Mathematica Scientia, 36(1), pp.203~214 (2016), Elsevier BV[DOI]
- N. Kerzman, "The Cauchy kernel, the Szego kernel and the Riemann mapping function", Math. Ann, 236(1), pp.85~93 (1971)
- N. Kerzman, "The Szego kernel in terms of Cauchy-Fantappie kernels", Duke Math. J, 45(2), pp.197~224 (1978)[DOI]
- Min Ku, "Half Dirichlet problem for the Hölder continuous matrix functions in Hermitian Clifford analysis", Complex Variables and Elliptic Equations, 58(7), pp.1037~1056 (2013), Informa UK Limited[DOI]
- M. Ku, "Half Dirichlet problem for matrix functions on the unit ball in Hermitian Clifford analysis", J. Math. Anal. Appl, 374(2), pp.442~457 (2011)[DOI]
- Dixan Peña-Peña, "Quaternionic Clifford Analysis: The Hermitian Setting", Complex Analysis and Operator Theory, 1(1), pp.97~113 (2007), Springer Science and Business Media LLC[DOI]
- G. Szegő, "Über orthogonale Polynome, die zu einer gegebenen Kurve der komplexen Ebene gehören", Mathematische Zeitschrift, 9(3-4), pp.218~270 (1921), Springer Science and Business Media LLC[DOI]