2 citations · 16 across the 65 of their papers we have counts for
23 papers · 1 filter
On the differentiability of the Sobolev norm of on compact Riemannian manifolds
Duvan Cardona, Julio Delgado, Andres Felipe Muñoz-Tello
In this work we study the differentiability for the Sobolev norm of in the sense of Gâteaux , where is an arbitrary closed Riemannian manifold.
-Maximal functions on graded Lie groups
Duván Cardona
Bourgain in his seminal paper [2] about the analysis of maximal functions associated to convex bodies, has estimated in a sharp way the -operator norm of the maximal function…
Schatten-von Neumann properties for Hörmander classes on compact Lie groups
Duván Cardona, Marianna Chatzakou, Michael Ruzhansky +1
Let be a compact Lie group of dimension In this work we characterise the membership of classical pseudo-differential operators on in the trace class ideal $S_{1}(L^2(G…
Boundedness of the dyadic maximal function on graded Lie groups
Duván Cardona, Julio Delgado, Michael Ruzhansky
Let and let It was proved independently by C. Calderón, R. Coifman and G. Weiss that the dyadic maximal function \begin{equation*} \mathcal{M}^{dσ}_Df(x…
Björk-Sjölin condition for strongly singular convolution operators on graded Lie groups
Duván Cardona, Michael Ruzhansky
In this work we extend the -Björk-Sjölin theory of strongly singular convolution operators to arbitrary graded Lie groups. Our criteria are presented in terms of the oscillati…
Oscillating singular integral operators on compact Lie groups revisited
Duván Cardona, Michael Ruzhansky
In [24, Theorem 2'] Charles Fefferman has proved the weak (1,1) boundedness for a class of oscillating singular integrals that includes the oscillating spectral multipliers of the…
Oscillating singular integral operators on graded Lie groups revisited
Duván Cardona, Michael Ruzhansky
In this work, we extend the Euclidean theory of oscillating singular integrals due to Fefferman and Stein in \cite{Fefferman1970,FeffermanStein1972} to arbitrary graded Lie groups.…
Fourier multipliers for Triebel-Lizorkin spaces on compact Lie groups
Duván Cardona, Michael Ruzhansky
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 Hörmander-Mihlin-Marcinkiewi…
Fourier multipliers for Triebel-Lizorkin spaces on graded Lie groups
Duván Cardona, Michael Ruzhansky
In this work we investigate the boundedness of Fourier multipliers on Triebel-Lizorkin spaces associated to positive Rockland operators on a graded Lie group. The found criterion i…
On the multiplier problem for the ball on graded Lie groups
Duván Cardona
In this note, we consider a non-commutative analogy of the classical Fefferman multiplier problem for the ball. More precisely, if is the characteristic function of the unit in…
Determinants and Plemelj-Smithies formulas
Duván Cardona, Julio Delgado, Michael Ruzhansky
We establish Plemelj-Smithies formulas for determinants in different algebras of operators. In particular we define a Poincaré type determinant for operators on the torus $\Tn$ and…
- bounds for pseudo-multipliers associated to the harmonic oscillator
Duván Cardona
In this note we investigate some conditions of Hörmander-Mihlin type in order to assure the - boundedness for pseudo-multipliers of the harmonic oscil…
Boundedness of pseudo-differential operators in subelliptic Sobolev and Besov spaces on compact Lie groups
Duván Cardona, Michael Ruzhansky
In this paper we investigate the Besov spaces on compact Lie groups in a subelliptic setting, that is, associated with a family of vector fields, satisfying the Hörmander condition…
The nuclear trace of periodic vector-valued pseudo-differential operators with applications to index theory
Duván Cardona, Vishvesh Kumar
In this paper, we investigate the nuclear trace of vector-valued Fourier multipliers on the torus and its applications to the index theory of periodic pseudo-differential operators…
The index of Toeplitz operators on compact Lie groups and simply connected closed 3-manifolds
Duván Cardona
In this paper we use the notion of operator-valued symbol in order to compute the index of Toeplitz operators on compact Lie groups. Our approach combines the Connes index theorem…
Hörmander condition for pseudo-multipliers associated to the harmonic oscillator
Duván Cardona, Michael Ruzhansky
In this paper we prove Hörmander-Mihlin multiplier theorems for pseudo-multipliers associated to the harmonic oscillator (also called the Hermite operator). Our approach can be ext…
A brief description of operators associated to the quantum harmonic oscillator on Schatten-von Neumann classes
Duvan Cardona
In this note we study pseudo-multipliers associated to the harmonic oscillator (also called Hermite multipliers) belonging to Schatten classes on . We also inves…
The weak type for convolution operators on locally compact groups
Duván Cardona
In this paper we provide necessary and sufficient conditions for the boundedness, of convolution operators on locally compact (Hausdorff) to…
Characterization of nuclear pseudo-multipliers associated to the harmonic oscillator
Duván Cardona, Edgardo Barraza
In this paper we study pseudo-multipliers associated to the harmonic oscillator (also called Hermite multipliers) belonging to the ideal of -nuclear operators on Lebesgue spaces…
Pseudo-differential operators on with applications to discrete fractional integral operators
Duván Cardona
In this manuscript we provide necessary and sufficient conditions for the boundedness, of discrete Fourier multipliers (Fourier multipliers…
Littlewood-Paley theorem, Nikolskii inequality, Besov spaces, Fourier and spectral multipliers on graded Lie groups
Duvan Cardona, Michael Ruzhansky
In this paper we investigate Besov spaces on graded Lie groups. We prove a Nikolskii type inequality (or the Reverse Hölder inequality) on graded Lie groups and as consequence we o…
Hölder-Besov boundedness for periodic pseudo-differential operators
Duván Cardona
In this work we give Hölder-Besov estimates for periodic Fourier multipliers. We present a class of bounded pseudo-differential operators on periodic Besov spaces with symbols of l…
Besov continuity for pseudo-differential operators on compact homogeneous manifolds
Duván Cardona
In this paper we study the Besov continuity of pseudo-differential operators on compact homogeneous manifolds We use the global quantization of these operators in terms of…