Riesz transforms on deformed Fock spaces
\(L^p\) spaces \((1< p<\infty)\) are considered on Fock-von Neumann algebras \(\Gamma_A(\mathbb{R}^n)\) and \(\Gamma_{A'}(\mathbb{R}^{2n})\), these algebras being equipped with their canonical traces. The paper extends known results on the \(L^p\) boundedness of some Riesz transforms \({\mathcal R}'= \nabla'N^{\prime-{1\over 2}}\) associated with a number operator \(N'\) and a gradient \(\nabla'\) such that \(\nabla^{\prime *}\nabla'= N'\).
scientific article; zbMATH DE number 1379886