On the reverse Hardy-type integral inequalities in the whole plane with the extended Riemann-Zeta function
Michael Th. Rassias, Yang Bi-cheng, А. М. Райгородский
Abstract
In the present paper, using weight functions we obtain some equivalent conditions of two kinds of the reverse Hardy-type integral inequalities with a nonhomogeneous kernel in the whole plane. The constant factors, which are related to the extended Riemann zeta function, are proved to be the best possible. In the form of applications, a few equivalent conditions of two kinds of the reverse Hardy-type integral inequalities with the homogeneous kernel in the whole plane are deduced. We also consider some particular cases.
Topics & Concepts
MathematicsType (biology)Riemann zeta functionRiemann hypothesisInequalityMathematical analysisPure mathematicsBiologyEcologyDifferential Equations and Boundary ProblemsMathematical functions and polynomialsAdvanced Harmonic Analysis Research