Author

Amiran Gogatishvili

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Preprint Aug 2026

Compact sets in Banach lattices over spaces of homogeneous type

We prove a Kolmogorov--Riesz compactness theorem for Banach lattices over spaces of homogeneous type. Especially, we consider the one for $L^1$. Our characterization is formulated in terms of boundedness, tightness, and approximation by averaging operators, which replace translations in the absence of a group structure...

Ayşenur Aydoğdu, Amiran Gogatishvili, Yoshihiro Sawano et al. · 0 citations

Preprint Aug 2026

The Hardy averaging operator between Orlicz spaces and a new gauge functional characterizing a given Orlicz space

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 other words, the optimal Orlicz domain is automatically the optimal r.i.\ domain. More generally, we show that every Luxemburg--Orlicz norm is e...

Amiran Gogatishvili, R. Kerman, S. Spektor · 1 citation