5 papers
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…
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…
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…
Stein-Weiss-Adams inequality on Morrey spaces
Aidyn Kassymov, Maria Alessandra Ragusa, Michael Ruzhansky +1
We establish Adams type Stein-Weiss inequality on global Morrey spaces on general homogeneous groups. Special properties of homogeneous norms and some boundedness results on global…
Hardy inequalities on constant-order noncommutative Vilenkin groups
Aidyn Kassymov, J. P Velasquez-Rodriguez
In this note we extend several integral inequalities to the context of noncommutative Vilenkin groups. We prove some sharp weak and strong type estimates for the Hardy operator and…