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Sharp results for the mean summability of Fourier series on compact Lie groups.

Leonardo, Giulini, Saverio Colzani — 1989

Mathematische Annalen

$L^{p} - L^{q}$ -estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. II.

Cowling, Michael; Giulini, Saverio; Meda, Stefano — 1995

Journal of Lie Theory

UC-sets in the dual object of compact groups

Saverio Giulini — 1980

Colloquium Mathematicae

A remark on the asymmetry of convolution operators

Saverio Giulini — 1989

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A convolution operator, bounded on $L^{q}(\mathbb{R}^{n})$ , is bounded on $L^{p}(\mathbb{R}^{n})$ , with the same operator norm, if $p$ and $q$ are conjugate exponents. It is well known that this fact is false if we replace $\mathbb{R}^{n}$ with a general non-commutative locally compact group $G$ . In this paper we give a simple construction of a convolution operator on a suitable compact group $G$ , wich is bounded on $L^{q}(G)$ for every $q\in[2,\infty)$ and is unbounded on $L^{p}(G)$ if $p\in[1,2)$ .

A remark on the asymmetry of convolution operators

Saverio Giulini — 1989

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Central Fourier Analysis for Lorentz Spaces on Compact Lie Groups.

Giancarlo Travaglini; Saverio Giulini — 1989

Monatshefte für Mathematik

Oscillating multipliers on noncompact symmetric spaces.

Saverio Giulini; Stefano Meda — 1990

Journal für die reine und angewandte Mathematik

The Martin compactification of the Cartesian product of two hyperbolic spaces.

Wolfgang Woess; Saverio Giulini — 1993

Journal für die reine und angewandte Mathematik

Lp multipliers on noncompact symmetric spaces.

G. Mauceri; Saverio Giulini; S. Meda — 1997

Journal für die reine und angewandte Mathematik

$L^{p} - L^{q}$ estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III

Michael Cowling; Saverio Giulini; Stefano Meda — 2001

Annales de l’institut Fourier

Let $X$ be a symmetric space of the noncompact type, with Laplace–Beltrami operator $- ℒ$ , and let $[b, \infty)$ be the $L^{2} (X)$ -spectrum of $ℒ$ . For $τ$ in $ℂ$ such that $Re τ \geq 0$ , let $𝒫_{τ}$ be the operator on $L^{2} (X)$ defined formally as $\exp (- τ {(ℒ - b)}^{1 / 2})$ . In this paper, we obtain $L^{p} - L^{q}$ operator norm estimates for $𝒫_{τ}$ for all $τ$ , and show that these are optimal when $τ$ is small and when $| \arg τ |$ is bounded below $π / 2$ .

Pointwise convergence of Fourier series on compact Lie groups

Leonardo Colzani; Saverio Giulini; Giancarlo Travaglini; Marco Vignati — 1990

Colloquium Mathematicae

Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth

Michael Cowling; Saverio Giulini; Andrzej Hulanicki; Giancarlo Mauceri — 1994

Studia Mathematica

We prove that on Iwasawa AN groups coming from arbitrary semisimple Lie groups there is a Laplacian with a nonholomorphic functional calculus, not only for $L^{1} (A N),$ but also for $L^{p} (A N)$ , where 1 < p < ∞. This yields a spectral multiplier theorem analogous to the ones known for sublaplacians on stratified groups.

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Currently displaying 1 – 12 of 12

Sharp results for the mean summability of Fourier series on compact Lie groups.

$L^{p} - L^{q}$ -estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. II.

UC-sets in the dual object of compact groups

A remark on the asymmetry of convolution operators

A remark on the asymmetry of convolution operators

Central Fourier Analysis for Lorentz Spaces on Compact Lie Groups.

Oscillating multipliers on noncompact symmetric spaces.

The Martin compactification of the Cartesian product of two hyperbolic spaces.

Lp multipliers on noncompact symmetric spaces.

$L^{p} - L^{q}$ estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III

Pointwise convergence of Fourier series on compact Lie groups

Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth