On Decomposition Theorems for Hardy Spaces on Domains in ℂn and Applications

Hardy spaces of analytic functions are studied both on strongly pseudoconvex domains in ℂⁿ and on domains of finite type in ℂ². Duality theorems, atomic decompositions, and factorization of functions are treated. Mapping properties of certain Hankel operators are studied.     

Zur Bestimmung der Alkalibenzoate und Salicylate

Ohne Zusammenfassung     

Geometric Lipschitz spaces and applications to complex function theory and nilpotent groups

It is known that a function on $\text{R}$ⁿ which can be well approximated by polynomials, in the mean over Euclidean balls, is Lipschitz smooth in the usual sense. In this paper an analogous theorem is proved in which $\text{R}$ⁿ is replaced by a set X, the averages over balls are replaced by a family of sublinear operators satisfying certain axioms, and the polynomials are replaced by a class of functions having certain regularity properties with respect to the averaging operators. Applications are given to function theory on domains in $\text{C}$ⁿ, to nilpotent Lie groups, and to the classical Euclidean case. The first application provides a characterization of the duals of Hardy spaces on the ball in $\text{C}$ⁿ.     

On functions in p-adic BMO and the distribution of prime integers

We study the spaces BMOp of functions of bounded mean oscillation modeled on a p-adic martingale, and determine their relationship with the ordinary, continuous space BMO of functions of bounded mean oscillation. Somewhat surprisingly, these results are related to information about the distribution of primes.