We apply a decomposition lemma of Uchiyama and results of the author to obtain good weighted Littlewood-Paley estimates for linear sums of functions satisfying reasonable decay, smoothness, and cancellation conditions. The heart of our application is a combinatorial trick treating m-fold dilates of dyadic cubes. We use our estimates to obtain new weighted inequalities for Bergman-type spaces defined on upper half-spaces in one and two parameters, extending earlier work of R. L. Wheeden and the author....
The main results of this paper may be loosely stated as follows.
Theorem.— Let and be sums of Galois algebras with group over algebraic number fields. Suppose that and have the same dimension and that they are identical at their wildly ramified primes. Then (writing for the maximal order in )
In...
Considering the ring of integers in a number field as a -module (where is a galois group of the field), one hoped to prove useful theorems about the extension of this module to a module or a lattice over a maximal order. In this paper it is show that it could be difficult to obtain, in this way, parameters which are independent of the choice of the maximal order. Several lemmas about twisted group rings are required in the proof.
The Alexander ideals of classical knots are characterised, a result which extends to certain higher dimensional knots.
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