General Weighted Opial Inequalities for Linear Differential Operators

Weighted Inequalities for Potential Operators on Differential Forms

On Weighted Norm Inequalities for Positive Linear Operators

Let T be a positive linear operator defined for nonnegative functions on a rj-finite measure space {X,m,fi). Given 1 < p < oo and a nonnegative weight function w on X , it is shown that there exists a nonnegative weight function v , finite /¿-almost everywhere on X , such that (1) I \Tf)*wdfi< j fvd/i, for all/>0, J x J x tere exists posi ( h if and only if th tive /¿-almost everywhere on X...

General Multiple Opial-type Inequalities for the Canavati Fractional Derivatives

In this paper we establish some general multiple Opial-type inequalities involving the Canavati fractional derivatives. In some cases the best possible constants are discussed. 1 Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Split, Croatia. E-mail address: [email protected] 2 Faculty of Textile Technology, University of Zagreb, Zagreb, Croatia. E-mail address:...

On Inequalities for Differential Operators

In this paper we study the following problem: Given that certain functionals of u and its derivatives belong to given Lclasses over the infinite interval, what can be said about the L-classes of other functionals? Utilizing a simple device from the theory of linear differential equations, we obtain a number of results due to Landau, Kolmogoroff, Halperin-von Neumann, and Nagy, together with som...

Weighted Norm Inequalities for Fractional Operators

We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relies upon a good-λ method that does not use any size or smoothness estimates for the kernels. Indiana Univ. Ma...