Given an irreducible symmetric cone \(\Omega\subset{\mathbb R}^n\), the analytic Besov \(p\)-space \({\mathbb B}^p(T_\Omega)\) over the tube domain \(T_\Omega :=\{ x+iy: \;x\in{\mathbb R}^n, \, y\in\Omega\}\) is defined as the family of all functions \(F\) in the Hardy space \({\mathcal H}(T_\Omega)\) such that \(\| F \|_{{\mathbb B}^p(T_\Omega)} := \| \triangle^m (y) \square^m F \|_{L^p (T_\Omega,d\lambda)} <\infty\) where \(\triangle(y)\) denotes the determinant function associated to \(\Omega\), \(\square\) is the differential operator defined by the equation \(\square[ e^{\langle z|\zeta\rangle}] = \triangle(\zeta)e^{\langle z|\zeta\rangle}\) and \(m\) is a the smallest integer with \(m > \max\{ 2n/r-1)/p, (n/r-1)(1-1/p)+1/p \}\) where \(r:=\text{rank}(\Omega)\).
The author proves that the norm \(\| \cdot \|_{{\mathbb B}^p(T_\Omega)}\) is invariant under the holomorphic automorphisms of \(T_\Omega\) whenever \(n\) is a multiple of the rank \(r\) and \(p>2-r/n\).