A remark on the asymmetry of convolution operators

Giulini, Saverio. "A remark on the asymmetry of convolution operators." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 83.1 (1989): 85-88. <http://eudml.org/doc/287510>.

@article{Giulini1989,
abstract = {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 $p \in [1,2)$.},
author = {Giulini, Saverio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Non-commutative groups; Convolution operators; Asymmetry; convolution; conjugate exponents; non-commutative locally compact group; compact group},
language = {eng},
month = {12},
number = {1},
pages = {85-88},
publisher = {Accademia Nazionale dei Lincei},
title = {A remark on the asymmetry of convolution operators},
url = {http://eudml.org/doc/287510},
volume = {83},
year = {1989},
}

TY - JOUR
AU - Giulini, Saverio
TI - A remark on the asymmetry of convolution operators
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1989/12//
PB - Accademia Nazionale dei Lincei
VL - 83
IS - 1
SP - 85
EP - 88
AB - 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 $p \in [1,2)$.
LA - eng
KW - Non-commutative groups; Convolution operators; Asymmetry; convolution; conjugate exponents; non-commutative locally compact group; compact group
UR - http://eudml.org/doc/287510
ER -