1.

Record Nr.

UNINA9910975326203321

Autore

González-Pérez Adrían M

Titolo

Singular Integrals in Quantum Euclidean Spaces

Pubbl/distr/stampa

Providence : , : American Mathematical Society, , 2021

©2021

ISBN

9781470467500

147046750X

Edizione

[1st ed.]

Descrizione fisica

1 online resource (110 pages)

Collana

Memoirs of the American Mathematical Society ; ; v.272

Classificazione

42B2042B3747G3046L5146L1081R60

Altri autori (Persone)

JungeMarius

ParcetJavier

Disciplina

515/.723

Soggetti

Singular integrals

Calderón-Zygmund operator

Pseudodifferential operators

Noncommutative differential geometry

Lp spaces

Quantum theory

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

Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Harmonic analysis and PDE

Operator theory -- Integral, integro-differential, and pseudodifferential operators -- Pseudodifferential operators

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

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

Quantum theory -- Groups and algebras in quantum theory -- Noncommutative geometry

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

"July 2021. Volume 272."

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

Quantum Euclidean spaces -- Calderón-Zygmund Lp theory -- Pseudodifferential Lp calculus -- Lp regularity for elliptic PDEs.



Sommario/riassunto

"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"--