Inequalities for the fractional convolution operator on differential forms

Convolution Inequalities for the Boltzmann Collision Operator

In this paper we study the integrability properties of a general version of the Boltzmann collision operator that includes inelastic interactions between particles. We prove a Young’s inequality for variable hard potentials, a Hardy-Littlewood-Sobolev inequality for soft potentials, and estimates with Maxwellian weights for variable hard potentials. In addition we obtain sharp constants for Max...

Differential Inequalities for Hybrid Fractional Differential Equations

In this paper, some basic fractional differential inequalities for a finite system of an IVP of hybrid fractional differential equations with linear perturbations of second type are proved. An existence and a comparison theorem for the considered hybrid fractional differential have also been established.

Subordination and Superordination Properties for Convolution Operator

In present paper a certain convolution operator of analytic functions is defined. Moreover, subordination and superordination- preserving properties for a class of analytic operators defined on the space of normalized analytic functions in the open unit disk is obtained. We also apply this to obtain sandwich results and generalizations of some known results.

The Harmonic Operator for Exterior Differential Forms.

Dirichlet to Neumann Operator on Differential Forms

We define the Dirichlet to Neumann operator on exterior differential forms for a compact Riemannian manifold with boundary and prove that the real additive cohomology structure of the manifold is determined by the DN operator. In particular, an explicit formula is obtained which expresses Betti numbers of the manifold through the DN operator. We express also the Hilbert transform through the DN...