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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.