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Now showing items 11-17 of 17
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 ...
Subelliptic Gevrey spaces
(Wiley, 2020)
In this paper, we define and study Gevrey spaces associated with a H\"ormander family of (globally defined) vector fields and its corresponding sub-Laplacian. We show some natural relations between the various Gevrey spaces ...
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 ...