1、哈爾濱工業(yè)大學(xué)碩士學(xué)位論文微分流形上的HardyLittlewood積分不等式姓名：朱海靜申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：運(yùn)籌學(xué)與控制論指導(dǎo)教師：包革軍20050601耋璽耋三些查耋耋蘭至圭耋堡蘭蘭AbstractDifferentiablemanifoldISoneofimportantbranchesofmathematic1tSconceptisinvolvedinmanydifferentmathematicalfieldsandith

2、aswideandeffectiveapplicationsintheoreticalphysics，especiallyingeneralrelativitytheoryandnormalfieldsDifferentiablemanifoldbecomesanimportanttoolinpromptingtodevelopingthesetheories，ithasbeenenduedgeometryalgebraandanaly

3、ticprovideastageandlanguagefornonlinearanalysisItslanguageisexteriordifferentialformonmanifoIdastherelationofEuclidspaceandclassicalanalytic，differentiablemanifoldhasmoregeneralapplicationinmanyfieldsandisoneoffundamentc

4、onceptoftypicalin20centuryInthispaperwhatwearetobespeakaboutaretheintegralinequalitiesofdifferentialformsthatisHardy—LittlewoodintegralinequalitiesHardyLittlewoodintegralinequalitieshavewideapplicationsinmanyfields，Sucha

5、spotentialtheoryharmonicanalysisandthetheoryofHp—spacesThepurposeofthispaperistOobtainHardy—LittlewoodintegralinequalitiesondifferentialmanifoldAccordingtothedomainwegivelocalintegralinequalitiesandglobalintegralinequali

6、tiesTheparametric群(Q卜weightedintegralinequalityisthemajorobjectsofdiscussion，butwewillgivetheHardy‘LittlewoodintegralinequalityabouttWO—weightedintegralinequalityand4(z)一weightedintegralinequalityKeywordsexterior；tangent