Analytic continuation and convolution of hypersingular higher Hilbert- Riesz kernels
The usual higher Hilbert-Riesz transforms are principal value convolution transforms with kernels \(Y_ j(x)| x|^{-j-n}\), where \(Y_ j\) is a homogeneous harmonic polynomial of degree j. The authors consider more generally the kernel \(x^ j| x|^{-j+\lambda -n}\), where for Re \(\lambda\) \(<0\), the expression is defined as a distribution by analytic continuation, and obtain a condition under which two such kernels can be convolved and formulas for the convolution.
scientific article; zbMATH DE number 4006946
scientific article