Inequalities of the form ∑∞ k=0 |f̂(mk)| k+1 ≤ C ‖f‖1 for all f ∈ H1, where {mk} are special subsequences of natural numbers, are investigated in the vector-valued setting. It is proved that Hardy’s inequality and the generalized Hardy inequality are equivalent for vector valued Hardy spaces defined in terms of atoms and that they actually characterize B-convexity. It is also shown that for 1 < ...

One gets more than two hundred papers when searching by the keywords “Hardy” and “inequality” in the review journals Zentralblatt für Mathematik or Mathematical Reviews. Almost half of these publications appeared after 1990. In the absolute majority, these papers deal with various generalizations, extensions and improvements of the wellknown Hardy inequality (HI) presented in monograph [8] (bot...

In this paper, we derive a generalized multiplicative Hardy-LittlewoodPolya type inequality, as well as several related additive inequalities, for functions of operators in Hilbert spaces. In addition, we find the modulus of continuity of a function of an operator on a class of elements defined with the help of another function of the operator. We then apply the results to solve the following p...

This paper provides novel generalizations by considering the generalized conformable fractional integrals for reverse Copson’s type inequalities on time scales. The main results will be proved using a general algebraic inequality, chain rule, Hölder’s and integration parts Our investigations unify extend some continuous their corresponding discrete analogues. In addition, when α = 1, we obtain ...

We investigated several novel conformable fractional gamma-nabla dynamic Hardy–Hilbert inequalities on time scales in this study. Several continuous and their corresponding discrete analogues the literature are combined expanded by these inequalities. Hölder’s inequality a few algebraic used to demonstrate our findings.