15 citations · 87 across the 48 of their papers we have counts for
50 papers
A solution to a conjecture on the norm of the Copson operator minus the Identity for monotone sequences
Achraf Ben Said, Amiran Gogatishvili
We investigate the operator distance between the Identity and the Copson operator on the cone of nonnegative, nonincreasing sequences within the Lebesgue sequence spaces $\ell^p(\m…
Compact sets in Banach lattices over spaces of homogeneous type
Ayşenur Aydoğdu, Amiran Gogatishvili, Yoshihiro Sawano +1
We prove a Kolmogorov--Riesz compactness theorem for Banach lattices over spaces of homogeneous type. Especially, we consider the one for . Our characterization is formulated…
On Weighted Local Morrey-type and Complementary Local Morrey-Type Spaces
Amiran Gogatishvili, Yoshihiro Sawano, Tuğçe Ünver
In this paper, we establish necessary and sufficient conditions for continuous embeddings between weighted local Morrey-type spaces and weighted complementary local Morrey-type spa…
The Hardy averaging operator between Orlicz spaces and a new gauge functional characterizing a given Orlicz space
Amiran Gogatishvili, Ron Kerman, Susanna Spektor
We prove that the largest Orlicz space into which the Hardy averaging operator maps coincides with the largest rearrangement-invariant (r.i.) space mapping into that space; in othe…
Interpolation of classical Lorentz spaces measuring oscillation
Amiran Gogatishvili, Julio S. Neves, Luboš Pick +1
We obtain an explicit characterization of the -functional of a pair of weighted classical Lorentz spaces of type . We develop a method for obtaining such characterization bas…
The Persson--Stepanov theorem revisited
Amiran Gogatishvili, Luboš Pick, Hana Turčinová +1
We develop a new proof of the result of L.-E.~Persson and V.D.~Stepanov \cite[Theorems 1 and 3]{Per:02}, which provides a characterization of a Hardy integral inequality involving…