Higher riesz transforms and derivatives of the riesz kernels

Abstract

Using the Riesz transforms, derivatives of the Riesz kernels, homogeneous harmonic polynomials and derivatives of the Newton kernel, we introduce four kinds of the higher Riesz transforms. Further we study relations among them. As one of the preparations we investigate homogeneous polynomials which appear in numerators of derivatives of the Riesz kernels.

Keywords:

• Higher Riesz transforms
• Riesz kernels
• Homogeneous polynomials