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

Mathematical Analysis

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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.

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Format: paperback
ASIN: 1470449374
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Analysis
Domain: Amazon UK
Release Date: 30 May 2022
Listed Since: 30 November 2021

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

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