7 papers
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…
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…
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 in…
boundedness of Fourier multipliers on quantum Euclidean spaces
M. Ruzhansky, S. Shaimardan, K. Tulenov
In this paper, we study Fourier multipliers on quantum Euclidean spaces and obtain results on their boundedness. On the way to get these results, we prove Paley, Hausdor…
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…
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…