In this paper we derive new inequalities involving the generalized Hardy operator. The obtained results known We also get classical Hardy–Hilbert inequality.

The principal objects of study in this thesis are the noncommutative Hardy algebras introduced by Muhly and Solel in 2004, also called simply “Hardy algebras,” and their quotients by ultraweakly closed ideals. The Hardy algebras form a class of nonselfadjoint dual operator algebras that generalize the classical Hardy algebra, the noncommutative analytic Toeplitz algebras introduced by Popescu i...

We have characterized 11 polymorphic microsatellite loci in the invasive ant Solenopsis invicta. Primer pairs were evaluated on fire ants collected from monogyne mounds in Lauderdale County, Mississippi. The observed and effective number of alleles ranged from two to six and from 1.31 to 2.64, respectively. The observed and expected heterozygosity values ranged from 0.1613 to 0.7826 and from 0....

We provide a careful treatment of the weak Hardy spaces Hp,∞(Rn) for all indices 0 < p < ∞. The study of these spaces presents differences from the study of the Hardy-Lorentz spaces H(R) for q <∞, due to the lack of a good dense subspace of them. We obtain several properties of weak Hardy spaces and we discuss a new square function characterization for them, obtained by He [16].

Abstract In this paper, we will study the Hardy and BMO spaces associated to generalized operator $$L_{\alpha }= (-\Delta )^{\alpha /2}+a|x|^{-\alpha }$$ L α = ( - Δ ) </mml:m...

Twenty microsatellite markers were isolated and characterized from the Chinese black sleeper, Bostrychus sinensis. Loci were screened in 30 individuals from Taiwan. For each locus, the number of alleles varied from 4 to 22 with mean expected and observed heterozygosity of 0.79 and 0.66, respectively. One locus significantly deviated from Hardy-Weinberg equilibrium after Bonferroni correction an...

Two electrophoretic forms of erythrocytic carbonic anhydrase were found to be controlled by one autosomal locus with two codominant alleles, CA(f) and CA(8). The gene frequencies for the CA(f) and CA(8) alleles were found to be.15 and.85, respectively, in a sample of 53 mice from Middlesex County, New Jersey. The observed genotypic frequencies indicated that the population was in Hardy-Weinberg...

Let $\mathcal{M}$ be the bilinear Hardy-Littlewood maximal function and $\vec{b}=(b,b)$ a collection of locally integrable functions. In this paper, authors establish characterizations weighted {\rm BMO} space in terms several different commutators function, respectively; these include iterated commutator $\mathcal{M}_{\Pi \vec{b}}$, linear $\mathcal{M}_{\Sigma\vec{b}}$, $[\Pi \vec{b},\mathcal{...

In this paper, we study the existence of extremal functions (pairs) following discrete Sobolev inequality (0.1) and Hardy-Littlewood-Sobolev (0.2) in lattice Z N : ? u ? q ? C p , D 1 ? ? ( ) where ? 3 < > ? = ? is a constant depending on ; ? i j ? f g | ? r s 0 + 2 . We introduce Concentration-Compactness principle, prove for best constants supercritical cases respectively.

We revise the genus Opisthoscelis Schrader, and erect the genus Tanyscelisgen. n. with Opisthoscelis pisiformis Froggatt as its type species. Species of both genera induce sexually dimorphic galls on Eucalyptus (Myrtaceae) in Australia, with Opisthoscelis subrotunda Schrader also in Papua New Guinea. We synonymise the following taxa (junior synonym with senior synonym): Opisthoscelis fibularis ...