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arXiv · 2602.00479

New characterizations of BLO spaces by heat semigroups and applications

Shaohong Liang·Dongyong Yang·Chao Zhang
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Abstract

In this paper, we give two new characterizations of the bounded lower oscillation (BLO) space by using the Gaussian heat semigroup. Using these characterizations, we prove the boundary lower-envelope estimate of the solutions of the heat equation with BLO boundary data, a Gaussian John-Nirenberg criterion and a quantitative estimates of the BLO-norm. Also, we reprove the BMO-BLO boundedness of the Littlewood-Paley $g$-function by using the semigroup method.

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Shaohong Liang, Dongyong Yang, Chao Zhang. 2026-01-31. New characterizations of BLO spaces by heat semigroups and applications. https://arxiv.org/abs/2602.00479

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