LEADER 04656nam 22008173 450 001 9910975326203321 005 20231110215743.0 010 $a9781470467500 010 $a147046750X 035 $a(CKB)4940000000616258 035 $a(MiAaPQ)EBC6798071 035 $a(Au-PeEL)EBL6798071 035 $a(RPAM)22493604 035 $a(PPN)259971316 035 $a(OCoLC)1275392622 035 $a(EXLCZ)994940000000616258 100 $a20211214d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSingular Integrals in Quantum Euclidean Spaces 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2021. 210 4$d©2021. 215 $a1 online resource (110 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.272 300 $a"July 2021. Volume 272." 311 08$a9781470449377 311 08$a1470449374 320 $aIncludes bibliographical references. 327 $aQuantum Euclidean spaces -- Caldero?n-Zygmund Lp theory -- Pseudodifferential Lp calculus -- Lp regularity for elliptic PDEs. 330 $a"We shall establish the core of singular integral theory and pseudodifferential calculus over the archetypal algebras of noncommutative geometry: quantum forms of Euclidean spaces and tori. Our results go beyond Connes' pseudodifferential calculus for rotation algebras, thanks to a new form of Calderon-Zygmund theory over these spaces which crucially incorporates nonconvolution kernels. We deduce Lp-boundedness and Sobolev p-estimates for regular, exotic and forbidden symbols in the expected ranks. In the L2 level both Calderon-Vaillancourt and Bourdaud theorems for exotic and forbidden symbols are also generalized to the quantum setting. As a basic application of our methods, we prove Lp-regularity of solutions for elliptic PDEs"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aSingular integrals 606 $aCaldero?n-Zygmund operator 606 $aPseudodifferential operators 606 $aNoncommutative differential geometry 606 $aLp spaces 606 $aQuantum theory 606 $aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Caldero?n-Zygmund, etc.)$2msc 606 $aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Harmonic analysis and PDE$2msc 606 $aOperator theory -- Integral, integro-differential, and pseudodifferential operators -- Pseudodifferential operators$2msc 606 $aFunctional analysis -- Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) -- Noncommutative measure and integration$2msc 606 $aFunctional analysis -- Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) -- General theory of von Neumann algebras$2msc 606 $aQuantum theory -- Groups and algebras in quantum theory -- Noncommutative geometry$2msc 615 0$aSingular integrals. 615 0$aCaldero?n-Zygmund operator. 615 0$aPseudodifferential operators. 615 0$aNoncommutative differential geometry. 615 0$aLp spaces. 615 0$aQuantum theory. 615 7$aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Caldero?n-Zygmund, etc.). 615 7$aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Harmonic analysis and PDE. 615 7$aOperator theory -- Integral, integro-differential, and pseudodifferential operators -- Pseudodifferential operators. 615 7$aFunctional analysis -- Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) -- Noncommutative measure and integration. 615 7$aFunctional analysis -- Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) -- General theory of von Neumann algebras. 615 7$aQuantum theory -- Groups and algebras in quantum theory -- Noncommutative geometry. 676 $a515/.723 686 $a42B20$a42B37$a47G30$a46L51$a46L10$a81R60$2msc 700 $aGonzález-Pérez$b Adrían M$01799715 701 $aJunge$b Marius$01643539 701 $aParcet$b Javier$01799716 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910975326203321 996 $aSingular Integrals in Quantum Euclidean Spaces$94344110 997 $aUNINA