In this note we consider a generalisation to the metric setting of the recent work (Gu and Yung in J Funct Anal 281:109075, 2021). In particular, we show that under relatively weak conditions on a metric measure space (X,d,ν), it holds true that (Formula presented.) where s is a generalised dimension associated to X and [·]Lwp is the weak Lebesgue norm. We provide some counterexamples which show that our assumptions are optimal.
A metric counterpart of the Gu–Yung formula / Buccheri, Stefano; Górny, Wojciech. - In: REVISTA MATEMÁTICA COMPLUTENSE. - ISSN 1139-1138. - (2025). [10.1007/s13163-025-00554-4]
A metric counterpart of the Gu–Yung formula
Stefano Buccheri
;
2025
Abstract
In this note we consider a generalisation to the metric setting of the recent work (Gu and Yung in J Funct Anal 281:109075, 2021). In particular, we show that under relatively weak conditions on a metric measure space (X,d,ν), it holds true that (Formula presented.) where s is a generalised dimension associated to X and [·]Lwp is the weak Lebesgue norm. We provide some counterexamples which show that our assumptions are optimal.File in questo prodotto:
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