A Note on Hardy Inequalities in Metric Measure Spaces for the Case p=1

Abstract

In this note, we announce the two-weight Hardy inequalities on metric measure spaces possessing a polar decomposition for the case p=1 and 1≤q<∞ obtained in the paper Ruzhansky et al. (Hardy inequalities on metric measure spaces, IV: The case p=1. Forum Mathematicum, 2024, to appear. https://doi.org/10.1515/forum-2023-0319.). We refer to Ruzhansky et al. (Hardy inequalities on metric measure spaces, IV: The case p=1. Forum Mathematicum, 2024, to appear. https://doi.org/10.1515/forum-2023-0319.) for the complete proofs and more details. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.