In this paper we continue our investigations of square function inequalities in harmonic analysis. Here we investigate oscillation and variation inequalities for singular integral operators in dimensions d ≥ 1. Our estimates give quantitative information on the speed of convergence of truncations of a singular integral operator, including upcrossing and λ jump inequalities.

The purpose of the present paper is to establish some new retarded weakly singular integral inequalities of Gronwall-Bellman type for discontinuous functions, which generalize some known weakly singular and impulsive integral inequalities. The inequalities given here can be used in the analysis of the qualitative properties of certain classes of singular differential equations and singular impu...

Fractional inequalities are useful in establishing the uniqueness of solution for partial differential equations of fractional order. Also they provide upper and lower bounds for solutions of fractional boundary value problems. In this paper we obtain some general integral inequalities containing generalized Mittag-Leffler function and some already known integral inequalities have been produced...

We present some new nonlinear integral inequalities Bellman-Bihari type with delay for discontinuous functions integro-sum inequalities; impulse integral inequalities . Some applications of the results are included: conditions of boundedness uniformly , stability by Lyapunov uniformly , practical stability by Chetaev uniformly for the solutions of impulsive differential and integrodifferential ...

In this paper we use a new approach to obtain a class of multivariable integral inequalities of Hilbert type from which we can recover as special cases integral inequalities obtained recently by Pachpatte and the present authors.

In this paper we present integral conductor inequalities connecting the Lorentz p, q-(quasi)norm of a gradient of a function to a one-dimensional integral of the p, q-capacitance of the conductor between two level surfaces of the same function. These inequalities generalize an inequality obtained by the second author in the case of the Sobolev norm. Such conductor inequalities lead to necessary...