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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

Singular Integrals in Quantum Euclidean Spaces cover

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