15 citations · 87 across the 48 of their papers we have counts for
35 papers · 1 filter
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…
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…
Weighted inequalities involving two Hardy operators
Amiran Gogatishvili, Tugce Ünver
We find necessary and sufficient conditions on weights , i.e. measurable, positive, and finite, a.e. on , for which there exists a positive constant …
On weighted Cesàro function spaces
Amiran Gogatishvili, Tuğçe Ünver
The main objective of this paper is to provide a comprehensive demonstration of recent results regarding the structures of the weighted Cesàro and Copson function spaces. These spa…