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Van der Corput lemmas for Mittag-Leffler functions. II. $α$-directions
(Elsevier, 2021-06)
The paper is devoted to study analogues of the van der Corput lemmas involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study ...
A comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups
(2021)
In this paper we present a comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups. Moreover, using the comparison principle we obtain blow-up type results and global in $t$-boundedness ...
Schatten-von Neumann classes of integral operators
(Elsevier, 2021)
In this work we establish sharp kernel conditions ensuring that the corresponding integral operators belong to Schatten-von Neumann classes. The conditions are given in terms of the spectral properties of operators acting ...
On a class of anharmonic oscillators
(Elsevier, 2021)
In this work we study a class of anharmonic oscillators within the framework of the Weyl-H\"ormander calculus. The anharmonic oscillators arise from several applications in mathematical physics as natural extensions of the ...
Fourier multipliers for Triebel-Lizorkin spaces on compact Lie groups
(Springer (part of Springer Nature), 2021)
We investigate the boundedness of Fourier multipliers on a compact Lie group when acting on Triebel-Lizorkin spaces. Criteria are given in terms of the H\"ormander-Mihlin-Marcinkiewicz condition. In our analysis, we use ...
$L^p$-$L^q$ boundedness of $(k, a)$-Fourier multipliers with applications to Nonlinear equations
(Oxford University Press, 2021)
The $(k,a)$-generalised Fourier transform is the unitary operator defined using the $a$-deformed Dunkl harmonic oscillator. The main aim of this paper is to prove $L^p$-$L^q$ boundedness of $(k, a)$-generalised Fourier ...
Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds with negative curvature
(Elsevier, 2021-10)
In this paper we obtain Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities with sharp constants on Riemannian manifolds with non-positive sectional curvature and, in particular, a variety of ...
Eigenfunction expansions of ultradifferentiable functions and ultradistributions. III. Hilbert spaces and Universality
(Springer, 2021-03)
In this paper we analyse the structure of the spaces of smooth type functions, generated by elements of arbitrary Hilbert spaces, as a continuation of the research in our previous papers in this series. We prove that these ...
Global Functional calculus, lower/upper bounds and evolution equations on manifolds with boundary
(2021-01-07)
Given a smooth manifold $M$ (with or without boundary), in this paper we establish a global functional calculus (without the standard assumption that the operators are classical pseudo-differential operators) and the ...
Harmonic and Anharmonic Oscillators on the Heisenberg Group
(Elsevier, 2021-05-25)
Although there is no canonical version of the harmonic oscillator on the Heisenberg group $\mathbf{H}_n$ so far, we make a strong case for a particular choice of operator by using the representation theory of the Dynin-Folland ...