5 citations · 13 across the 11 of their papers we have counts for
13 papers
Compactness and Spectral Properties of Multiplier Operators in the Walsh System
Michael Ruzhansky, Sergo A. Episkoposian, Rafik Yeghoyan
We investigate compactness and spectral properties of multiplier operators associated with the Walsh system in the spaces , . Building upon previously establi…
Lieb-Thirring inequalities for the Dirac operator on spheres
Uwe Kähler, André Pedroso Kowacs, Michael Ruzhansky
In this paper, we obtain bounds for the best constants in two inequalities which can be seen as analogues of the Lieb-Thirring inequality, but with the Dirac operator, on the s…
Fujita exponents on quantum Euclidean spaces
Edward McDonald, Michael Ruzhansky, Serikbol Shaimardan +1
We study the well-posedness of a non-linear heat equation with power nonlinearity with positive initial data on quantum Euclidean spaces. We prove a noncommutative analogue of the…
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…
Fourier multipliers and their applications to PDE on the quantum Euclidean space
M. Ruzhansky, S. Shaimardan, K. Tulenov
In this work, we present some applications of the - boundedness of Fourier multipliers to PDEs on the noncommutative (or quantum) Euclidean space. More precisely, we esta…
Hormander-Mikhlin type theorem on non-commutative spaces
Rauan Akylzhanov, Michael Ruzhansky, Kanat Tulenov
In this paper, we introduce a Fourier-type formalism on non-commutative spaces. As a result, we obtain two versions of Hormander-Mikhlin Lp-multiplier theorem: on locally compact K…
Zero modes and Dirac-(logarithmic) Sobolev-type inequalities
Marianna Chatzakou, Uwe Kahler, Michael Ruzhansky
We study the decay rate of the zero modes of the Dirac operator with a matrix-valued potential that is considered here without any regularity assumptions, compared to the existing…
Sobolev inequality and its applications to nonlinear PDE on noncommutative Euclidean spaces
Michael Ruzhansky, Serikbol Shaimardan, Kanat Tulenov
In this work, we study the Sobolev inequality on noncommutative Euclidean spaces. As a simple consequence, we obtain the Gagliardo-Nirenberg type inequality and as its application…
A note on - boundedness of Fourier multipliers on noncommutative spaces
Michael Ruzhansky, Kanat Tulenov
In this work, we study Fourier multipliers on noncommutative spaces. In particluar, we show a simple proof of - estimate of Fourier multipliers on general noncommutative…
Bilinear Hardy inequalities on metric measure spaces
Michael Ruzhansky, Anjali Shriwastawa, Daulti Verma
In this paper, we discuss the Hardy inequality with bilinear operators on general metric measure spaces. We give the characterization of weights for the bilinear Hardy inequality t…
On geometric properties of -spaces on unitary duals of compact groups
Meiram Akhymbek, Michael Ruzhansky
In this paper, we study geometric properties of -spaces associated with the unitary dual of a compact group. More precisely, we prove uniform smoothness, uniform convexit…
Sharp upper bound for anisotropic Rényi entropy and Heisenberg uncertainty principle
Marianna Chatzakou, Michael Ruzhansky, Anjali Shriwastawa
In this paper, we prove the anisotropic Shannon inequality for the Renyi entropy with the best constant on Folland-Stein homogeneous Lie groups. As a consequence, we also prove the…
Hörmander type Fourier multiplier theorem and Nikolskii inequality on quantum tori, and applications
Michael Ruzhansky, Serikbol Shaimardan, Kanat Tulenov
In this paper, we study Hörmander type Fourier multiplier theorem and the Nikolskii inequality on quantum tori. On the way to obtain these results, we also prove some classical ine…