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...

Let G/H be a compactly causal symmetric space with causal compactification Φ : G/H → Š1, where Š1 is the BergmanŠilov boundary of a tube type domain G1/K1. The Hardy space H2(C) of G/H is the space of holomorphic functions on a domain Ξ(C) ⊂ GC/HC with L-boundary values on G/H. We extend Φ to imbed Ξ(C) into G1/K1, such that Ξ(C) = {z ∈ G1/K1 | ψm(z) = 0}, with ψm explicitly known. We use this ...

We review and extend a recent suggestion that fine-scale localization of a disease-susceptibility locus for a complex disease be done on the basis of deviations from Hardy-Weinberg equilibrium among affected individuals. This deviation is driven by linkage disequilibrium between disease and marker loci in the whole population and requires a heterogeneous genetic basis for the disease. A finding...

In this paper, the authors obtain continuity of a class linear operators on variable anisotropic Hardy--Lorentz spaces. addition, also that dual space Hardy-Lorentz spaces is BMO-type with exponents. This result still new even when exponent function $p(\cdot)$ $p$.

We established some new α-conformable dynamic inequalities of Hardy–Knopp type. Some generalizations Hardy type in two variables on time scales are established. Furthermore, we investigated Hardy’s inequality for several functions calculus. Our results proved by using two-dimensional Jensen’s and Fubini’s theorem scales. When α=1, then obtain well-known time-scale due to Hardy. As special cases...

This note deals with the inequality (∫ b a |u(x)|w0(x)dx )1/q ≤ C (∫ b a |u(x)|wk(x)dx )1/p , (1) more precisely, with conditions on the parameters p > 1, q > 0 and on the weight functions w0, wk (measurable and positive almost everywhere) which ensure that (1) holds for all functions u from a certain class K with a constant C > 0 independent of u. Here −∞ ≤ a < b ≤ ∞ and k ∈ N and we will cons...

for every u∈W1,p(Rn). It is easy to see that the proposition fails when s > 1, where s = q/p. In this paper we are trying to find out what happens if s > 1. We show that it does not only become true but obtains better estimates. The described result is stated and proved in Section 3. The method invoked is different from that by Cazenave in [2]; it relies on some Littlewood-Paley theory and Beso...

We relate Orlicz-Hardy inequalities on a bounded Euclidean domain to certain fatness conditions on the complement. In the case of certain log-scale distortions of Ln, this relationship is necessary and sufficient, thus extending results of Ancona, Lewis, and Wannebo. 0. Introduction Suppose Ω ⊂ R is a bounded domain and let d(x) = dist(x, ∂Ω). We consider integral Hardy inequalities (0.1) ∀u ∈ ...