Singular Integrals in Quantum Euclidean Spaces
Marius Junge author Javier Parcet author Adrian M Gonzalez-Perez author
Format:Paperback
Publisher:American Mathematical Society
Published:30th May '22
Should be back in stock very soon
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 Calder´on-Zygmund theory over these spaces which crucially incorporates nonconvolution kernels. We deduce Lp-boundedness and Sobolev p-estimates for regular, exotic and forbidden symbols in the expected ranks. In the L2 level both Calder´on-Vaillancourt and Bourdaud theorems for exotic and forbidden symbols are also generalized to the quantum setting. As a basic application of our methods, we prove Lp-regularity of solutions for elliptic PDEs.
ISBN: 9781470449377
Dimensions: unknown
Weight: 204g