Weighted norm inequalities for the Opdam–Cherednik transform

Weighted Norm Inequalities

Introduction In the rst part of the paper we study integral operators of the form (1) Kf(x) = v(x) x Z 0 k(x; y)u(y)f(y) dy; x > 0; where the real weight functions v(t) and u(t) are locally integrable and the kernel k(x; y) 0 satisses the following condition: there exists a constant D 1 such that Standard examples of a kernel k(x; y) 0 satisfying (2) are (i) k(x; y) = (x ? y) , 0 (ii) k(x; y) =...

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

Weighted norm inequalities for integral transforms

Weighted (L, L) inequalities are studied for a variety of integral transforms of Fourier type. In particular, weighted norm inequalities for the Fourier, Hankel, and Jacobi transforms are derived from Calderón type rearrangement estimates. The obtained results keep their novelty even in the simplest cases of the studied transforms, the cosine and sine Fourier transforms. Sharpness of the condit...

Weighted Norm Inequalities for the Local Sharp Maximal Function