Singular Integrals in Quantum Euclidean Spaces(English, Paperback, Gonzalez-Perez Adrian M.)

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Singular Integrals in Quantum Euclidean Spaces(English, Paperback, Gonzalez-Perez Adrian M.) is written by Gonzalez-Perez Adrian M. and published by American Mathematical Society. It's available with International Standard Book Number or ISBN identification 1470449374 (ISBN 10) and 9781470449377 (ISBN 13).

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.