A Note on the Oseen Kernels

The Oseen operators are ∆∂xj ∂xke , where ∆ is the standard Laplace operator and t ∈ R+. We give an explicit expression for the kernels of these Fourier multipliers which involves the incomplete gamma function and the confluent hypergeometric functions of the first kind. This explicit expression provides directly the classical decay estimates with sharp bounds. Although the computations are elementary and the definition of the Oseen kernels goes back to the 1911 paper of this author, we were not able to find the simple explicit expression below in the literature.