We give a systematic study on the Hardy spaces of functions with values in the non-commutative L-spaces associated with a semifinite von Neumann algebra M. This is motivated by the works on matrix valued Harmonic Analysis (operator weighted norm inequalities, operator Hilbert transform), and on the other hand, by the recent development on the non-commutative martingale inequalities. Our non-com...

Survival after freezing was measured for seeds and germinants of four seedlots each of interior spruce (Picea glauca x engelmannii complex), lodgepole pine (Pinus contorta Dougl. ex Loud.), Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) and western red cedar (Thuja plicata Donn ex D. Donn). Effects of eight seed treatments on post-freezing survival of seeds and germinants were tested: dry, ...

We consider approximation of L p functions by Hardy functions on subsets of the circle. We rst derive some properties of traces of Hardy classes on such subsets, and then turn to a generalization of classical extremal problems involving norm constraints on the complementary subset. Approximation dans l'espace de Hardy de fonctions L p sur un sous{ensemble du cercle R esum e : Nous etudions l'ap...

Let P be a linear, elliptic second order symmetric operator, with an associated quadratic form q, and let W be a potential such that the Hardy inequality λ0 ∫ Ω Wu 2 ≤ q(u) holds with (non-negative) best constant λ0. We give sufficient conditions so that the spectrum of the operator 1 W P is [λ0,∞). In particular, we apply this to several well-known Hardy inequalities: (improved) Hardy inequali...

The main purpose of this paper is to briefly review the earlier works of multiparameter Hardy space theory and boundedness of singular integral operators on such spaces defined on product of Euclidean spaces, and to describe some recent developments in this direction. These recent works include discrete multiparameter Calderón reproducing formulas and Littlewood-Paley theory in the framework of...

* Correspondence: [email protected] Department of Engineering Sciences and Mathematics, LuleåUniversity of Technology SE 971 87 Luleå, Sweden Full list of author information is available at the end of the article Abstract First we present and discuss an important proof of Hardy’s inequality via Jensen’s inequality which Hardy and his collaborators did not discover during the 10 years of research ...

In this paper, we introduce the p-adic Hardy type operator and obtain its sharp bound on the p-adic Lebesgue product spaces. Meanwhile, an analogous result is computed for the p-adic Lebesgue product spaces with power weights. In addition, we characterize a sufficient and necessary condition which ensures that the weighted p-adic Hardy type operator is bounded on the p-adic Lebesgue product spa...

Despite a true antipathy to the subject Hardy contributed deeply to modern probability. His work with Ramanujan begat probabilistic number theory. His work on Tauberian theorems and divergent series has probabilistic proofs and interpretations. Finally Hardy spaces are a central ingredient in stochastic calculus. This paper reviews his prejudices and accomplishments through these examples. ∗Dep...

Using a multivariable Faa di Bruno formula we give conditions on transformations τ : [0, 1] → X where X is a closed and bounded subset of R such that f ◦ τ is of bounded variation in the sense of Hardy and Krause for all f ∈ C(X ). We give similar conditions for f◦τ to be smooth enough for scrambled net sampling to attain O(n−3/2+ ) accuracy. Some popular symmetric transformations to the simple...

The paper studies the weighted weak type inequalities for the Hardy operator as an operator from weighted L to weighted weak L in the case p = 1. It considers two different versions of the Hardy operator and characterizes their weighted weak type inequalities when p = 1. It proves that for the classical Hardy operator, the weak type inequality is generally weaker when q < p = 1. The best consta...