Sharp weighted bounds for fractional integral operators

Sharp Weighted Bounds for Fractional Integral Operators

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal...

Bounds for Singular Fractional Integrals and Related Fourier Integral Operators

On weighted inequalities for certain fractional integral operators

and Dn denotes the derivative operator ∂/∂x1, . . . ,∂xn. The operators in (1.1) provide multidimensional generalizations to the well-known one-dimensional Riemann-Liouville andWeyl fractional integral operators defined in [5] (see also [1]). The paper [7] considers several formulas and interesting properties of (1.1). By invoking the Gauss hypergeometric function 2F1(α,β;γ;x), the following ge...

Weighted Estimates for Bilinear Fractional Integral Operators and Their Commutators

In this paper we will prove several weighted estimates for bilinear fractional integral operators and their commutators with BMO functions. We also prove maximal function control theorem for these operators, that is, we prove the weighted Lp norm is bounded by the weighted Lp norm of a natural maximal operator when the weight belongs to A∞. As a corollary we are able to obtain new weighted esti...

Some Weighted Integral Inequalities for Generalized Conformable Fractional Calculus

In this paper, we have obtained weighted versions of Ostrowski, Čebysev and Grüss type inequalities for conformable fractional integrals which is given by Katugompola. By using the Katugampola definition for conformable calculus, the present study confirms previous findings and contributes additional evidence that provide the bounds for more general functions.