Michael Ruzhansky

activity

20032023

most citedGlobal quantization of pseudo-differential operators on compact Lie groups, SU(2) and 3-sphere

115 citations · 1.9k across the 226 of their papers we have counts for

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99 papers · 1 filter

math.FA2023

A note on the polar decomposition in metric spaces

Zhirayr Avetisyan, Michael Ruzhansky

The analogue of polar coordinates in the Euclidean space, a polar decomposition in a metric space, if well-defined, can be very useful in dealing with integrals with respect to a s…

math.FA2023

Stein-Weiss-Adams inequality on Morrey spaces

Aidyn Kassymov, Maria Alessandra Ragusa, Michael Ruzhansky +1

We establish Adams type Stein-Weiss inequality on global Morrey spaces on general homogeneous groups. Special properties of homogeneous norms and some boundedness results on global…

math.FA2023

Asymptotic estimates for the growth of deformed Hankel transform by modulus of continuity

Vishvesh Kumar, Joel E. Restrepo, Michael Ruzhansky

We derive asymptotic estimates for the growth of the norm of the deformed Hankel transform on the deformed Hankel--Lipschitz space defined via a generalised modulus of continuity.…

math.FA2023

Elements (functions) that are universal with respect to a minimal system

Zhirayr Avetisyan, Martin Grigoryan, Michael Ruzhansky

We call an element $U$ conditionally universal for a sequential convergence space $Ω$ with respect to a minimal system ${φ_{n}}_{n = 1}^{\infty}$ in a continuously and densely e…

math.FA2023

Revised logarithmic Sobolev inequalities of fractional order

Marianna Chatzakou, Michael Ruzhansky

In this short note we prove the logarithmic Sobolev inequality with derivatives of fractional order on $R^{n}$ with an explicit expression for the constant. Namely, we show…

math.FA2023

Schatten-von Neumann properties for Hörmander classes on compact Lie groups

Duván Cardona, Marianna Chatzakou, Michael Ruzhansky +1

Let $G$ be a compact Lie group of dimension $n .$ In this work we characterise the membership of classical pseudo-differential operators on $G$ in the trace class ideal $S_{1}(L^2(G…

math.FA2023

Boundedness of the dyadic maximal function on graded Lie groups

Duván Cardona, Julio Delgado, Michael Ruzhansky

Let $1 < p \leq \infty$ and let $n \geq 2.$ It was proved independently by C. Calderón, R. Coifman and G. Weiss that the dyadic maximal function \begin{equation*} \mathcal{M}^{dσ}_Df(x…

math.FA2022★ 2 cited

Multidimensional Frank-Laptev-Weidl improvement of the Hardy Inequality

Prasun Roychowdhury, Michael Ruzhansky, Durvudkhan Suragan

We establish a new improvement of the classical $L^{p}$ -Hardy inequality on the multidimensional Euclidean space in the supercritical case. Recently, in [14], there has been a new ki…

math.FA2022

An Update On The $L^{p}$ - $L^{q}$ Norms of Spectral Multipliers on Unimodular Lie Groups

David Rottensteiner, Michael Ruzhansky

This note gives a wide-ranging update on the multiplier theorems by Akylzhanov and the second author [J. Funct. Anal., 278 (2020), 108324]. The proofs of the latter crucially rely…

math.FA2022★ 3 cited

Titchmarsh theorems on Damek-Ricci spaces via moduli of continuity of higher order

Manoj Kumar, Vishvesh Kumar, Michael Ruzhansky

A classical theorem of Titchmarsh relates the $L^{2}$ -Lipschitz functions and decay of the Fourier transform of the functions. In this note, we prove the Titchmarsh theorem for Damek…

math.FA2022★ 1 cited

Björk-Sjölin condition for strongly singular convolution operators on graded Lie groups

Duván Cardona, Michael Ruzhansky

In this work we extend the $L^{1}$ -Björk-Sjölin theory of strongly singular convolution operators to arbitrary graded Lie groups. Our criteria are presented in terms of the oscillati…

math.FA2022

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…

math.FA2022

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.…

math.FA2021

On a class of anharmonic oscillators II. General case

Marianna Chatzakou, Julio Delgado, Michael Ruzhansky

In this work we study a class of anharmonic oscillators on $R^{n}$ corresponding to Hamiltonians of the form $A (D) + V (x)$ , where $A (ξ)$ and $V (x)$ are $C^{\infty}$ functions…

math.FA2021

$L^{p}$ - $L^{q}$ Multipliers on commutative hypergroups

Vishvesh Kumar, Michael Ruzhansky

The main purpose of this paper is to prove Hörmander's $L^{p}$ - $L^{q}$ boundedness of Fourier multipliers on commutative hypergroups. We carry out this objective by establishing Paley…

math.FA2021

Titchmarsh theorems, Hausdorff-Young-Paley inequality and $L^{p}$ - $L^{q}$ boundedness of Fourier multipliers on harmonic $N A$ groups

Vishvesh Kumar, Michael Ruzhansky

In this paper we extend classical Titchmarsh theorems on the Fourier transform of H $o ¨$ lder-Lipschitz functions to the setting of harmonic $N A$ groups, which relate sm…

math.FA2021★ 9 cited

Hardy inequalities on metric measure spaces, II: The case $p > q$

Michael Ruzhansky, Daulti Verma

In this note we continue giving the characterisation of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since th…

math.FA2021

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…

math.FA2021★ 2 cited

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…

math.FA2021★ 21 cited

$L^{p}$ - $L^{q}$ boundedness of $(k, a)$ -Fourier multipliers with applications to Nonlinear equations

Vishvesh Kumar, Michael Ruzhansky

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 $L^{p}$ - $L^{q}$ bounde…

math.FA2020

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…

math.FA2020★ 4 cited

Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type inequalities for some fractional derivatives

Aidyn Kassymov, Michael Ruzhansky, Niyaz Tokmagambetov +1

In this paper we show different inequalities for fractional order differential operators. In particular, the Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type…

math.FA2020★ 3 cited

Hardy-Littlewood inequality and $L^{p}$ - $L^{q}$ Fourier multipliers on compact hypergroups

Vishvesh Kumar, Michael Ruzhansky

This paper deals with the inequalities devoted to the comparison between the norm of a function on a compact hypergroup and the norm of its Fourier coefficients. We prove the class…

math.FA2020★ 6 cited

$L^{p}$ - $L^{q}$ boundedness of pseudo-differential operators on smooth manifolds and its applications to nonlinear equations

Duván Cardona Sánchez, Vishvesh Kumar, Michael Ruzhansky +1

In this paper we study the boundedness of global pseudo-differential operators on smooth manifolds. By using the notion of global symbol we extend a classical condition of Hörmande…

A note on the polar decomposition in metric spaces

Stein-Weiss-Adams inequality on Morrey spaces

Asymptotic estimates for the growth of deformed Hankel transform by modulus of continuity

Elements (functions) that are universal with respect to a minimal system

Revised logarithmic Sobolev inequalities of fractional order

Schatten-von Neumann properties for Hörmander classes on compact Lie groups

Boundedness of the dyadic maximal function on graded Lie groups

Multidimensional Frank-Laptev-Weidl improvement of the Hardy Inequality

An Update On The Lp-Lq Norms of Spectral Multipliers on Unimodular Lie Groups

Titchmarsh theorems on Damek-Ricci spaces via moduli of continuity of higher order

Björk-Sjölin condition for strongly singular convolution operators on graded Lie groups

Oscillating singular integral operators on compact Lie groups revisited

Oscillating singular integral operators on graded Lie groups revisited

On a class of anharmonic oscillators II. General case

Lp-Lq Multipliers on commutative hypergroups

Titchmarsh theorems, Hausdorff-Young-Paley inequality and Lp-Lq boundedness of Fourier multipliers on harmonic NA groups

Hardy inequalities on metric measure spaces, II: The case p>q

Fourier multipliers for Triebel-Lizorkin spaces on compact Lie groups

Fourier multipliers for Triebel-Lizorkin spaces on graded Lie groups

Lp-Lq boundedness of (k,a)-Fourier multipliers with applications to Nonlinear equations

Determinants and Plemelj-Smithies formulas

Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type inequalities for some fractional derivatives

Hardy-Littlewood inequality and Lp-Lq Fourier multipliers on compact hypergroups

Lp-Lq boundedness of pseudo-differential operators on smooth manifolds and its applications to nonlinear equations

An Update On The $L^{p}$ - $L^{q}$ Norms of Spectral Multipliers on Unimodular Lie Groups

$L^{p}$ - $L^{q}$ Multipliers on commutative hypergroups

Titchmarsh theorems, Hausdorff-Young-Paley inequality and $L^{p}$ - $L^{q}$ boundedness of Fourier multipliers on harmonic $N A$ groups

Hardy inequalities on metric measure spaces, II: The case $p > q$

$L^{p}$ - $L^{q}$ boundedness of $(k, a)$ -Fourier multipliers with applications to Nonlinear equations

Hardy-Littlewood inequality and $L^{p}$ - $L^{q}$ Fourier multipliers on compact hypergroups

$L^{p}$ - $L^{q}$ boundedness of pseudo-differential operators on smooth manifolds and its applications to nonlinear equations