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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

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Vectorial Splitting Rational Lp Inequalities for Integral Operators

Journal of Applied Nonlinear Dynamics 2(1) (2012) 59--81 | DOI:10.5890/JAND.2012.09.005

George A. Anastassiou

Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.

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Here we present Lp, p>1, vectorial integral inequalitites for products of multivariate convex and increasing functions applied to vectors of ratios of functions. As applications we derive a wide range of vectorial fractional inequalities of Hardy type. They involve the left and right Erdelyi-Kober fractional integrals and left and right mixed Riemann-Liouville fractional multiple integrals. Also we give vectorial inequalities for Riemann-Liouville, Caputo, Canavati radial fractional derivatives. Some inequalities are of exponential type.


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