Weak-type estimates for the modified Hankel transform

The Hankel transform

Matlab code for the Discrete Hankel Transform

L and weak L estimates for the maximal Riesz transform and the maximal Beurling transform

We prove L estimates for the maximal Riesz transform in terms of the Riesz transform itself, for 1 < p ≤ ∞. We show that the corresponding weak L1 estimate fails for the maximal Riesz transform, but surprisingly does hold for the maximal Beurling transform.

Transformations Preserving the Hankel Transform

Transformations Preserving the Hankel Transform Christopher French Department of Mathematics and Statistics Grinnell College Grinnell, IA 50112 USA [email protected] Abstract We classify all polynomial transformations of integer sequences which preserve the Hankel transform, thus generalizing examples due to Layman and Spivey & Steil. We also show that such transformations form a group ...

Estimates for the Generalized Fourier-Bessel Transform in the Space L2

Some estimates are proved for the generalized Fourier-Bessel transform in the space (L^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.