Suppose E is a subset of the unit circle T and H∞ ⊂ L∞ is the Hardy subalgebra. We examine the problem of finding the distance from the characteristic function of E to znH∞. This admits an alternate description as a dual extremal problem. Precise solutions are given in several important cases. The techniques used involve the theory of Toeplitz and Hankel operators as well as the construction of...

We extensively analyze the maintenance of genetic variation and deviations from Hardy-Weinberg frequencies at a diallelic locus under mixed mating with apomixis and constant viability selection. Analytical proofs show that: (1) at most one polymorphic equilibrium exists, (2) polymorphism requires overdominant or underdominant selection, and (3) a simple, modified overdominance condition is suff...

We give a sufficient condition for limiting Sobolev and Hardy inequalities to hold on stratified homogeneous groups. In the Euclidean case, this reduces known cancelling necessary condition. obtain in particular endpoint Korn-Sobolev Korn-Hardy

by the method of weight coefficients and techniques of real analysis, ahardy-hilbert-type inequality with a general homogeneous kernel and a bestpossible constant factor is given. the equivalent forms, the operatorexpressions with the norm, the reverses and some particular examples are alsoconsidered.

Consider the second order divergence form elliptic operator L with complex bounded coefficients. In general, the operators related to it (such as Riesz transform or square function) lie beyond the scope of the Calderón-Zygmund theory. They need not be bounded in the classical Hardy, BMO and even some Lp spaces. In this work we generalize the classical approach and develop a theory of Hardy and ...

The Hardy space on the unit ball in C provides examples of a quasi-free, finite rank Hilbert module which contains a pure submodule isometrically isomorphic to the module itself. For n = 1 the submodule has finite codimension. In this note we show that this phenomenon can only occur for modules over domains in C and for finitely-connected domains only for Hardy-like spaces, the bundle shifts. M...

Studies of stem water in red-osier dogwood (Cornus stolonifera Michx.) using nuclear magnetic resonance spectroscopy indicated that most freezing occurs at temperatures above -30 C in cold-hardy and tender stems. Hardy and tender stems had about the same amount of unfrozen water at -40 C (0.28 gram of water per gram dry weight). When hardy stems were slowly cooled below -20 C, the temperature b...

Résumé Dans cet article, on étudie les fonctions maximales de Hardy–Littlewood pour une grande famille de mesures sur les variétés cuspidales. En particulier, on étudie une famille de variétés à croissance exponentielle du volume sur lesquelles la fonction maximale centrée de Hardy–Littlewood est de type faible (1,1), et la fonction maximale non-centrée de Hardy–Littlewood est bornée sur Lp pou...