Logarithmic-Sobolev and multilinear Hölder’sine qualities via heat flow monotonicity formulas

Abolarinwa, Abimbola and Oladejo, N. K. and Salawu, S. O. and Onate, C.A (2019) Logarithmic-Sobolev and multilinear Hölder’sine qualities via heat flow monotonicity formulas. Applied Mathematics and Computation, 364. ISSN 0096-3003

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Abstract

Heatflowmonotonicityformulashaveevolvedinrecentyearsasapowerfultoolinderiv-ingfunctionalandgeometricinequalitieswhichareinturnusefulinmathematicalanalysisandapplications.ThispaperaimsmainlyatprovingLogarithmicSobolevandmultilinearHölder’sinequalitiesthroughtheheatflowmethod.Precisely,twoentropymonotonicityformulasareconstructedviatheheatflow.Itisshownthatthefirstentropymonotonic-ityformulaisintimatelyrelatedtotheconcavityofthepowerofShannonentropyandFisherInformation,fromwhichtheassociatedlogarithmicSobolevinequalityforprobabil-itymeasureinEuclideansettingisrecovered.Thesecondmonotonicityformulacombinesverywellwithconvolutionanddiffusionsemigrouppropertiesoftheheatkerneltoestab-lishtheproofofthemultilinearHölderinequalities

Item Type: Article
Subjects: Q Science > QA Mathematics
Depositing User: Mr DIGITAL CONTENT CREATOR LMU
Date Deposited: 18 Sep 2019 10:07
Last Modified: 18 Sep 2019 10:07
URI: https://eprints.lmu.edu.ng/id/eprint/2236

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