Introduction to interpolation spaces

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1、AnIntroductiontoInterpolationTheoryDottoratodiRicercainMatematica,consorzioMilano-Insubria-Parma-TriesteAlessandraLunardiFebruary20072Contents1Realinterpolation71.1TheK-method..................................71.1.1Examples.................................121.1

2、.2Exercises.................................181.2Thetracemethod.................................191.2.1Exercises.................................241.3Intermediatespacesandreiteration.......................241.3.1Examples.................................301.3.2A

3、pplications.ThetheoremsofMarcinkiewiczandStampacchia...311.3.3Exercises.................................342Complexinterpolation352.1Definitionsandproperties............................372.1.1Examples.................................432.1.2ThetheoremsofHausdorff–Y

4、oung,Riesz–Thorin,Stein.......452.1.3Exercises.................................473Interpolationanddomainsofoperators493.1Operatorswithraysofminimalgrowth.....................493.1.1Twoormoreoperators..........................543.1.2Exercises....................

5、.............583.2ThecasewhereAgeneratesasemigroup....................583.2.1Examplesandapplications.Schaudertypetheorems.........624Powersofpositiveoperators674.1Definitionsandgeneralproperties........................674.1.1Powersofnonnegativeoperators.........

6、...........754.2Operatorswithboundedimaginarypowers...................764.2.1Exercises.................................814.2.2Thesumoftwooperatorswithboundedimaginarypowers.....824.2.3Exercises.................................874.3M-accretiveoperatorsinHilberts

7、paces.....................884.3.1Self-adjointoperatorsinHilbertspaces.................935Analyticsemigroupsandinterpolation995.1Characterizationofrealinterpolationspaces..................1005.2Generationofanalyticsemigroupsbyinterpolation..............1025.3Reg

8、ularityinabstractparabolicequations...................103345.4ApplicationstoregularityinparabolicPDE’s.................110ATheBochnerintegral113A.1Integralsovermeasurablerea