On fractional inequalities on metric measure spaces with polar decomposition

Kassymov A. Ruzhansky M. Zaur G.
1 July 2025 Walter de Gruyter GmbH

Forum Mathematicum
2025 #37 Issue 4 1035 - 1048 pp.

In this paper, we prove the fractional Hardy inequality on polarisable metric measure spaces. The integral Hardy inequality for 1 < p ≤ q < ∞ 1
fractional Hardy inequality , fractional Hardy-Sobolev type inequality , fractional Nash type inequality , Heisenberg group , homogeneous groups , logarithmic Hardy-Sobolev inequality , Metric measure spaces , polar decomposition

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Institute of Mathematics and Mathematical Modeling, 28 Shevchenko str., Almaty, 050010, Kazakhstan
Department of Mathematics: Analysis,Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Al-Farabi Kazakh National University, 71 Al-Farabi ave., Almaty, 050040, Kazakhstan

Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis
School of Mathematical Sciences
Al-Farabi Kazakh National University

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