15 citations · 87 across the 48 of their papers we have counts for
8 papers · 1 filter
Weighted inequalities for sub-monotone functionals
Amiran Gogatishvili, Luboš Pick
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals whic…
On the embedding between the variable Lebesgue space and the Orlicz space
David Cruz-Uribe, Amiran Gogatishvili, Tengiz Kopaliani
We give a sharp sufficient condition on the distribution function, , , of the exponent function that implies the embed…
The two-weight Hardy inequality: a new elementary and universal proof
Amiran Gogatishvili, Luboš Pick
We give a~new proof of the known criteria for the inequality \begin{equation*} \left(\int_{0}^{\infty}\left(\int_{0}^{t}f\right)^{q}w(t)\,dt\right)^{\frac{1}{q}} \leq C \left(\int_…
Characterizations of Besov and Triebel-Lizorkin Spaces via Averages on Balls
Feng Dai, Amiran Gogatishvili, Dachun Yang +1
Let and . In this article, the authors prove that the sequence consisting of the differences between $…
Weighted iterated Hardy-type inequalities
Amiran Gogatishvili, Rza Mustafayev
In this paper a reduction and equivalence theorems for the boundedness of the composition of a quasilinear operator with the Hardy and Copson operators in weighted Lebesgue spa…
A note on boundedness of the Hardy-Littlewood maximal operator on Morrey spaces
A. Gogatishvili, R. Ch. Mustafayev
In this paper we prove that the Hardy-Littlewood maximal operator is bounded on Morrey spaces $\mathcal{M}_{1,λ}(\rn)$, $0 \le \la < n$ for radial, decreasing functions on $\rn$