Singular integrals in quantum Euclidean spaces
著者
書誌事項
Singular integrals in quantum Euclidean spaces
（Memoirs of the American Mathematical Society, no. 1334）
American Mathematical Society, c2021
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注記
"July 2021, volume 272, number 1334 (fourth of 7 numbers)"
Includes bibliographical references (p. 87-90)
内容説明・目次
内容説明
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 Calderon-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 Calderon-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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