A New Hilbert-Type Inequality with Positive Homogeneous Kernel and Its Equivalent Forms
Bicheng Yang, Shanhe Wu, Aizhen Wang
Abstract
We establish a new inequality of Hilbert-type containing positive homogeneous kernel ( min { m , n } ) λ and derive its equivalent forms. Based on the obtained Hilbert-type inequality, we discuss its equivalent forms and give the operator expressions in some particular cases.
Topics & Concepts
MathematicsHomogeneousKernel (algebra)InequalityType (biology)Reproducing kernel Hilbert spaceOperator (biology)Pure mathematicsHilbert spaceMathematical analysisCombinatoricsBiochemistryRepressorEcologyBiologyTranscription factorGeneChemistryMathematical Inequalities and ApplicationsMathematics and ApplicationsAnalytic and geometric function theory