Wavelet analysis on a Boehmian space.
Weak-type estimates for the modified Hankel transform
We use the Galé and Pytlik [3] representation of Riesz functions to prove the Hörmander multiplier theorem for the modified Hankel transform.
Weierstrass transform associated with the Hankel operator.
Weighted bounded mean oscillation and the Hilbert transform
Weighted estimates for the Hankel-, - and - transformations
We give conditions on pairs of non-negative functions and which are sufficient that, for ,
Weighted inequalities for the Hilbert transform and the adjoint operator in the continuous case
Weighted inequalities through factorization.
In [4] P. Jones solved the question posed by B. Muckenhoupt in [7] concerning the factorization of Ap weights. We recall that a non-negative measurable function w on Rn is in the class Ap, 1 < p < ∞ if and only if the Hardy-Littlewood maximal operator is bounded on Lp(Rn, w). In what follows, Lp(X, w) denotes the class of all measurable functions f defined on X for which ||fw1/p||Lp(X) < ∞, where X is a measure space and w is a non-negative measurable function on X.It has recently...
Weighted norm inequalities for generalized Hankel conjugate transformations
Weighted norm inequalities for the -transformation.
Weighted weak type Hardy inequalities with applications to Hilbert transforms and maximal functions
Weighted-BMO and the Hilbert transform
In 1967, E. M. Stein proved that the Hilbert transform is bounded from to BMO. In 1976, Muckenhoupt and Wheeden gave an analogue of Stein’s result. They gave a necessary and sufficient condition for the boundedness of the Hilbert transform from . We improve the results of Muckenhoupt and Wheeden’s and give a necessary and sufficient condition for the boundedness of the Hilbert transform from to .
When is a Riesz distribution a complex measure?
Let be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by . I give an elementary proof of the necessary and sufficient condition for to be a locally finite complex measure (= complex Radon measure).
Wiener type theorem for regular operators of bounded support