Singular integrals in quantum Euclidean spaces - González-Pérez, Adrían Manuel; Junge, Marius; Parcet, Javier (Memoirs of the American Mathematical Society, 2021)
We shall establish the core of singular integral theory and pseudodifferential calculus over the archetypal algebras of noncommutative geometry: quantum forms of Euclidean spaces and tori. Our results go beyond Connes’ pseudodifferential calculus for rotation algebras, thanks to a new form of Calderón-Zygmund theory over these spaces which crucially incorporates nonconvolution kernels. We deduce