Two special applications of Riesz products
Riesz products have been in use for constructing measures for a long time. Sometimes only a subset of the thus produced measures satisfy the desired properties. Here two such cases will be examined. The first pertains to the uniform integrability of partial sums and consists of examining the known three instances of Riesz-like products generating such measures.
The second—and more substantial part—investigates to what extent the Fourier–Stieltjes transform of a Riesz product defines a Hankel–Littlewood multiplier on the space $L(\ell^2(\mathbb N))$ of operators.