03625nam 2200649 450 991082864920332120170822144223.01-4704-0475-3(CKB)3360000000465055(EBL)3114228(SSID)ssj0000889112(PQKBManifestationID)11452882(PQKBTitleCode)TC0000889112(PQKBWorkID)10875637(PQKB)10831991(MiAaPQ)EBC3114228(RPAM)14636281(PPN)195417607(EXLCZ)99336000000046505520150417h20072007 uy 0engur|n|---|||||txtccrOn necessary and sufficient conditions for Lp-estimates of Riesz transforms associated to elliptic operators on Rn and related estimates /Pascal AuscherProvidence, Rhode Island :American Mathematical Society,2007.©20071 online resource (102 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 186, Number 871"Volume 186, Number 871 (first of five numbers)."0-8218-3941-1 Includes bibliographical references.""Contents""; ""Acknowledgements""; ""Introduction""; ""Notation""; ""Chapter 1. Beyond Caldero'n-Zygmund operators""; ""Chapter 2. Basic L[sup(2)] theory for elliptic operators""; ""2.1. Definition""; ""2.2. Holomorphic functional calculus on L[sup(2)]""; ""2.3. L[sup(2)] off-diagonal estimates""; ""2.4. Square root""; ""2.5. The conservation property""; ""Chapter 3. L[sup(P)] theory for the semigroup""; ""3.1. Hypercontr activity and uniform boundedness""; ""3.2. W[sup(1,p)] elliptic estimates and hypercontr activity""; ""3.3. Gradient estimates""; ""3.4. Summary""""3.5. Sharpness issues""""3.6. Analytic extension""; ""Chapter 4. L[sup(p)] theory for square roots""; ""4.1. Riesz transforms on L[sup(p)]""; ""4.2. Reverse inequalities""; ""4.3. Invertibility""; ""4.4. Applications""; ""4.5. Riesz transforms and Hodge decomposition""; ""Chapter 5. Riesz transforms and functional calculi""; ""5.1. Blunck & Kunstmann's theorem""; ""5.2. Hardy-Littlewood-Sobolev estimates""; ""5.3. The Hardy-Littlewood-Sobolev-Kato diagram""; ""5.4. More on the Kato diagram""; ""Chapter 6. Square function estimates""""6.1. Necessary and sufficient conditions for boundedness of vertical square functions""""6.2. On inequalities of Stein and Fefferman for non-tangential square functions""; ""Chapter 7. Miscellani""; ""7.1. Local theory""; ""7.2. Higher order operators and systems""; ""Appendix A. Calderon-Zygmund decomposition for Sobolev functions""; ""Appendix. Bibliography""Memoirs of the American Mathematical Society ;Volume 186, Number 871.Singular integralsLittlewood-Paley theoryCalderón-Zygmund operatorElliptic operatorsSemigroupsSingular integrals.Littlewood-Paley theory.Calderón-Zygmund operator.Elliptic operators.Semigroups.515/.2331.46bclAuscher Pascal282068MiAaPQMiAaPQMiAaPQBOOK9910828649203321On necessary and sufficient conditions for Lp-estimates of Riesz transforms associated to elliptic operators on Rn and related estimates3958919UNINA