Multidimensional fourier and hartley transforms-are they same?

Multidimensional Hartley transforms with two different kernels namely the multi kernel and single kernel versions and their relation with the multidimensional Fourier transform are investigated. The multi kernel multidimensional Hartley transform is mathematically correct and it is equally applicable to all fields. On the other hand the single kernel representation of the multidimensional Hartley transform is mathematically incorrect despite the fact that it is fully equivalent to the multidimensional Fourier transform. Therefore, mathematically incorrect version of the multidimensional Hartley transform with a single kernel representation and the corresponding Fourier transform are not the same.