Weighted norm inequalities for the g-Littlewood-Paley operators associated with Laplace-Bessel differential operators

On Some Weighted Norm Inequalities for Littlewood–paley Operators

It is shown that the Lw,1< p<∞, operator norms of Littlewood–Paley operators are bounded by a multiple of ‖w‖ Ap , where γp = max{1, p/2} 1 p−1 . This improves previously known bounds for all p > 2. As a corollary, a new estimate in terms of ‖w‖Ap is obtained for the class of Calderón–Zygmund singular integrals commuting with dilations.

Sharp weighted norm inequalities for Littlewood–Paley operators and singular integrals

We prove sharp Lp(w) norm inequalities for the intrinsic square function (introduced recently by M. Wilson) in terms of the Ap characteristic of w for all 1 < p <∞. This implies the same sharp inequalities for the classical Lusin area integral S(f ), the Littlewood–Paley g-function, and their continuous analogs Sψ and gψ . Also, as a corollary, we obtain sharp weighted inequalities for any conv...

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...

Weighted norm inequalities for singular integral operators

Littlewood-paley Theorem for Schrödinger Operators

Let H be a Schrödinger operator on R. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces as well as Sobolev spaces in terms of dyadic functions of H . This generalizes and strengthens the previous result when the ...