Abstract
In this paper, we introduce the space \(\mathrm{BLO}^p(\omega )\) and establish the John–Nirenberg inequality for \(\mathrm{BLO}^p(\omega )\) with \(0<p\le 1\). As a corollary, it is proved that \(\mathrm{BLO}^p(\omega )\) are independent of the scale \(p\in (0,\infty )\) in sense of norm. Moreover, we characterize the weighted \(\mathrm{BLO}\) space through the reverse Hölder class. As applications, we will discuss the behavior of Littlewood–Paley operators in weighted \(\mathrm{BMO}\) space.
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Supported by the National Natural Science Foundation of China (No. 11671397).
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Zhao, H., Liu, Z. The John–Nirenberg Inequality of Weighted BLO Space and Its Applications. J Geom Anal 32, 66 (2022). https://doi.org/10.1007/s12220-021-00823-w
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DOI: https://doi.org/10.1007/s12220-021-00823-w