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Singular integrals in quantum Euclidean spaces

by Junge, Marius , González-Pérez, Adrían Manuel , Parcet, Javier

in Calderón-Zygmund operator / Calderón-Zygmund operator / Functional analysis -- Selfadjoint operator algebras ($C$-algebras, von Neumann ($W$-) algebras, etc.) -- General theory of von Neumann algebras. msc / Functional analysis -- Selfadjoint operator algebras ($C$-algebras, von Neumann ($W$-) algebras, etc.) -- Noncommutative measure and integration. msc / Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Harmonic analysis and PDE. msc / Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Calderón-Zygmund, etc.). msc / Lp spaces / Noncommutative differential geometry / Operator theory -- Integral, integro-differential, and pseudodifferential operators -- Pseudodifferential operators. msc / Pseudodifferential operators / Quantum theory / Quantum theory -- Groups and algebras in quantum theory -- Noncommutative geometry. msc / Singular integrals

2021

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Singular integrals in quantum Euclidean spaces

by Junge, Marius , González-Pérez, Adrían Manuel , Parcet, Javier

2021

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Singular integrals in quantum Euclidean spaces

by Junge, Marius , González-Pérez, Adrían Manuel , Parcet, Javier

2021

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Singular integrals in quantum Euclidean spaces

Junge, Marius,

González-Pérez, Adrían Manuel,

Parcet, Javier

2021

Overview

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 Calderón-Zygmund theory over these spaces which crucially incorporates nonconvolution kernels. We deduce

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Publisher

American Mathematical Society

Subject

Calderón-Zygmund operator

/ Calderón-Zygmund operator

/ Functional analysis -- Selfadjoint operator algebras ($C$-algebras, von Neumann ($W$-) algebras, etc.) -- General theory of von Neumann algebras. msc

/ Functional analysis -- Selfadjoint operator algebras ($C$-algebras, von Neumann ($W$-) algebras, etc.) -- Noncommutative measure and integration. msc

/ Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Harmonic analysis and PDE. msc

/ Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Calderón-Zygmund, etc.). msc

/ Lp spaces