In this paper, by using the Euler-Maclaurin expansion for the zeta function and estimating the weight function effectively, we derive a strengthenment of a Hardy-Hilbert’s type inequality proved by W.Y. Zhong. As applications, some particular results are considered.

The authors prove that bilinear operators given by finite sums of products of Calderón-Zygmund operators on Rn are bounded from HK̇11 q1 × HK̇ α2,p2 q2 into HK̇ q if and only if they have vanishing moments up to a certain order dictated by the target space. Here HK̇ q are homogeneous Herz-type Hardy spaces with 1/p = 1/p1 +1/p2, 0 < pi ≤ ∞, 1/q = 1/q1 +1/q2, 1 < q1, q2 < ∞, 1 ≤ q < ∞, α = α1 + α2 a...

In this paper a reduction and equivalence theorems for the boundedness of the composition of a quasilinear operator T with the Hardy and Copson operators in weighted Lebesgue spaces are proved. New equivalence theorems are obtained for the operator T to be bounded in weighted Lebesgue spaces restricted to the cones of monotone functions, which allow to change the cone of non-decreasing function...

We consider the valued field K := R((Γ)) of generalised series (with real coefficients and monomials in a totally ordered multiplicative group Γ ). We investigate how to endow K with a series derivation, that is a derivation that satisfies some natural properties such as commuting with infinite sums (strong linearity) and (an infinite version of) Leibniz rule. We characterize when such a deriva...

We consider the valued field K := R((Γ)) of generalized series (with real coefficients and monomials in a totally ordered multiplicative group Γ ). We investigate how to endow K with a series derivation, that is a derivation that satisfies some natural properties such as commuting with infinite sums (strong linearity) and (an infinite version of) Leibniz rule. We characterize when such a deriva...

We consider the valued fieldK := R((Γ)) of generalised series (with real coefficients and monomials in a totally ordered multiplicative group Γ ). We investigate how to endow K with a series derivation, that is a derivation that satisfies some natural properties such as commuting with infinite sums (strong linearity) and (an infinite version of) Leibniz rule. We characterize when such a derivat...

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 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 ...

In this paper, Jensen’s inequality and Fubini’s Theorem are extended for the function of several variables via diamond integrals time scale calculus. These extensions used to generalize Hardy-type inequalities with general kernels variables. Some Hardy Hilbert Polya Knop type also discussed as special cases. Classical new deduced from main results using particular scales.