Singular Integrals in Quantum Euclidean Spaces (Memoirs of the American Mathematical Society, 272)

By Adrían M. González-Pérez

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.

• Format: Paperback
• Language: English
• ISBN: 1470449374
• ISBN13: 9781470449377
• Release Date: November 2021
• Publisher: American Mathematical Society
• Length: 90 Pages
• Weight: 0.45 lbs.
• Dimensions: 0.8" x 7.0" x 10.0"