6 citations · 15 across the 18 of their papers we have counts for
21 papers
Fujita exponent for heat equation with Hörmander vector fields
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this paper, we show global existence and non-existence results for the heat equation with some of the squares of smooth vector fields on $\Rn$ satisfying Hörmander's rank condit…
Berezin-Li-Yau inequality for mixed local-nonlocal Dirichlet-Laplacian
Aidyn Kassymov, Berikbol T. Torebek
In this paper, we consider an eigenvalue problem for mixed local-nonlocal Laplacian $$\mathcal{L}^{a,b}_{\Om}:=-aΔ+b(-Δ)^s,\,a>0,\,b\in\mathbb{R},\,s\in (0,1),$$ with Dirichlet bou…
Fractional Hardy type inequalities on homogeneous Lie groups in the case
Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan
In this paper, we obtain a fractional Hardy inequality in the case on homogeneous Lie groups, and as an application we show the corresponding uncertainty principle. Also, we…
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…
Functional inequalities on symmetric spaces of noncompact type and applications
Aidyn Kassymov, Vishvesh Kumar, Michael Ruzhansky
The aim of this paper is to begin a systematic study of functional inequalities on symmetric spaces of noncompact type of higher rank. Our first main goal of this study is to estab…
Hardy inequalities on metric measure spaces, III: The case and applications
Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan
In this paper, we obtain a reverse version of the integral Hardy inequality on metric measure space with two negative exponents. Also, as for applications we show the reverse Hardy…
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…
Liouville theorems for Kirchhoff-type hypoelliptic Partial Differential Equations and systems. I. Heisenberg group
Aidyn Kassymov, Michael Ruzhansky, Niyaz Tokmagambetov +1
In this paper, we show the nonexistence results for the Kirchhoff elliptic, parabolic, and hyperbolic type equations on the Heisenberg groups. Also, the pseudo-parabolic and pseudo…
Logarithmic Hardy-Rellich inequalities on Lie groups
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this paper we obtain logarithmic Hardy and Rellich inequalities on general Lie groups. In the case of graded groups, we also show their refinements using the homogeneous Sobolev…
Logarithmic Sobolev-type inequalities on Lie groups
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this paper we show a number of logarithmic inequalities on several classes of Lie groups: log-Sobolev inequalities on general Lie groups, log-Sobolev (weighted and unweighted),…
Anisotropic Shannon inequality
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this note we prove the anisotropic version of the Shannon inequality. This can be conveniently realised in the setting of Folland and Stein's homogeneous groups. We give two pro…
Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type inequalities for some fractional derivatives
Aidyn Kassymov, Michael Ruzhansky, Niyaz Tokmagambetov +1
In this paper we show different inequalities for fractional order differential operators. In particular, the Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type…
Rayleigh-Faber-Krahn, Lyapunov and Hartmann-Wintner inequalities for fractional elliptic problems
Aidyn Kassymov, Michael Ruzhansky, Berikbol T. Torebek
In this paper in the cylindrical domain we consider a fractional elliptic operator with Dirichlet conditions. We prove, that the first eigenvalue of the fractional elliptic operato…
Reverse Stein-Weiss, Hardy-Littlewood-Sobolev, Hardy, Sobolev and Caffarelli-Kohn-Nirenberg inequalities on homogeneous groups
Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan
In this note we prove the reverse Stein-Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogen…
Reverse integral Hardy inequality on metric measure spaces
Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan
In this note, we obtain a reverse version of the integral Hardy inequality on metric measure spaces. Moreover, we give necessary and sufficient conditions for the weighted reverse…
Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups
Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan
In this note we prove the Stein-Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous nor…
Anisotropic fractional Gagliardo-Nirenberg, weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type inequalities, and applications to Riesz potentials and -sub-Laplacian systems
Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan
In this paper we prove the fractional Gagliardo-Nirenberg inequality on homogeneous Lie groups. Also, we establish weighted fractional Caffarelli-Kohn-Nirenberg inequality and Lyap…
Some functional inequalities for the fractional p-sub-Laplacian
Aidyn Kassymov, Durvudkhan Suragan
In this paper we study the fractional Dirichlet p-sub-Laplacian in a Haar measurable set on homogeneous Lie groups. We prove fractional Sobolev and Hardy inequalities and we also p…