Weighted inequalities for singular integral operators on the half-line

Weighted norm inequalities for singular integral operators

Weighted Norm Inequalities for Maximally Modulated Singular Integral Operators

We present a framework that yields a variety of weighted and vector-valued estimates for maximally modulated Calderón-Zygmund singular (and maximal singular) integrals from a single a priori weak type unweighted estimate for the maximal modulations of such operators. We discuss two approaches, one based on the good-λ method of Coifman and Fefferman [CF] and an alternative method employing the s...

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 norm inequalities for singular integral operators satisfying a variant of Hörmander’s condition

In this paper we establish weighted norm inequalities for singular integral operators with kernel satisfying a variant of the classical Hörmander’s condition.

Weighted Inequalities for Integral Operators with Some Homogeneous Kernels

In this paper we study integral operators of the form Tf(x) = |x − a1y| −α1 . . . |x − amy| mf(y) dy, α1 + . . . + αm = n. We obtain the L (w) boundedness for them, and a weighted (1, 1) inequality for weights w in Ap satisfying that there exists c > 1 such that w(aix) 6 cw(x) for a.e. x ∈ n , 1 6 i 6 m. Moreover, we prove ‖Tf‖BMO 6 c‖f‖∞ for a wide family of functions f ∈ L( ).