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math.AP2024
On fractional inequalities on metric measure spaces with polar decomposition
Aidyn Kassymov, Michael Ruzhansky, Gulnur Zaur
In this paper, we prove the fractional Hardy inequality on polarisable metric measure spaces. The integral Hardy inequality for is playing a key role in the proo…
math.AP2024
On global solutions of heat equations with time-dependent nonlinearities on unimodular Lie groups
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this work, we study the global well-posedeness of the heat equation with variable time-dependent nonlinearity of the form on unimodular Lie groups when the differenti…
math.AP2023
Logarithmic Sobolev, Hardy and Poincaré inequalities on the Heisenberg group
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this paper we first prove a number of important inequalities with explicit constants in the setting of the Heisenberg group. This includes the fractional and integer Sobolev, Ga…