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

in order to evaluation of the relationship among protein markers and traits such as proline content variation, quantum efficiency of photosystem ii and field viability index, 20 genotypes of barely were studied in a randomized complete block design in the greenhouse experiment. plants were transferred to springhouse at the four leaf stage and were located at the temperature of 4°c for three wee...

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 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].

We introduce a new class of Hardy spaces H(R), called Hardy spaces of Musielak-Orlicz type, which generalize the Hardy-Orlicz spaces of Janson and the weighted Hardy spaces of Garćıa-Cuerva, Strömberg, and Torchinsky. Here, φ : R × [0,∞) → [0,∞) is a function such that φ(x, ·) is an Orlicz function and φ(·, t) is a MuckenhouptA∞ weight. A function f belongs to H(R) if and only if its maximal fu...

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...

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 ...