 Bessel potential

The Bessel potential of order $s$ is the Fourier multiplier $(1+|\xi {|}^2{)}^{-s/2}$. Sufficiently high order turns a compactly supported finite-order distribution into a bounded continuous function.

Bessel potentials are a type of potential operator associated with Bessel functions, which are solutions to Bessel's differential equation. In functional analysis and partial differential equations, Bessel potentials are used to define certain types of Sobolev spaces and are closely related to the notion of fractional derivatives. The Bessel potential of order \( \alpha \) can be defined in terms of the Bessel operator.