Address:
Department of Mathematics, University of Arkansas, Fayetteville, AR 72701, USA
Departamento de Matemáticas, Universidad Simón Bolívar, Caracas, Venezuela
E-mail:
jx1004@uark.edu
jryan@uark.edu
cvanegas@usb.ve
Abstract: In this paper we deal with Rarita-Schwinger type operators on spheres and real projective space. First we define the spherical Rarita-Schwinger type operators and construct their fundamental solutions. Then we establish that the projection operators appearing in the spherical Rarita-Schwinger type operators and the spherical Rarita-Schwinger type equations are conformally invariant under the Cayley transformation. Further, we obtain some basic integral formulas related to the spherical Rarita-Schwinger type operators. Second, we define the Rarita-Schwinger type operators on the real projective space and construct their kernels and Cauchy integral formulas.
AMSclassification: primary 30G35; secondary 53C27.
Keywords: spherical Rarita-Schwinger type operators, Cayley transformation, real projective space, Almansi-Fischer decomposition, Iwasawa decomposition.
DOI: 10.5817/AM2012-4-271