Fractional cartesian products of sets

@article{Blei1979,
abstract = {Let $E$ be a subset of a discrete abelian group whose compact dual is $G$. $E$ is exactly $p$-Sidon (respectively, exactly non-$p$-Sidon) when$(*)\hspace\{142.26378pt\}C_E(G)^\wedge \subset \ell ^r$ holds if and only if $r\in [p,\infty ]$ (respectively, $r\in (p,\infty )$). $E$ is said to be exactly $\Lambda ^\beta $ (respectively, exactly non-$\Lambda ^\beta $) if $E$ has the property$(**)\hspace\{28.45274pt\}\text\{every\} \displaystyle \{f\in L^2_E(G) \text\{satisfies\} \int _G \{\rm exp\} (\lambda |f|^\{2/\alpha \}< \infty , \text\{for\} \text\{all\} \lambda >0,\}$ if and only if $\alpha \in [\beta ,\infty )$ (respectively, $\alpha \in (\beta ,\infty )$).In this paper, for every $p\in [1,2)$ and $\beta \in [1,\infty )$, we display sets which are exactly $p$-Sidon, exactly non-$p$-Sidon, exactly $\Lambda ^\beta $ and exactly non-$\Lambda ^\beta $.},
author = {Blei, Ron C.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {79-105},
publisher = {Association des Annales de l'Institut Fourier},
title = {Fractional cartesian products of sets},
url = {http://eudml.org/doc/74413},
volume = {29},
year = {1979},
}

TY - JOUR
AU - Blei, Ron C.
TI - Fractional cartesian products of sets
JO - Annales de l'institut Fourier
PY - 1979
PB - Association des Annales de l'Institut Fourier
VL - 29
IS - 2
SP - 79
EP - 105
AB - Let $E$ be a subset of a discrete abelian group whose compact dual is $G$. $E$ is exactly $p$-Sidon (respectively, exactly non-$p$-Sidon) when$(*)\hspace{142.26378pt}C_E(G)^\wedge \subset \ell ^r$ holds if and only if $r\in [p,\infty ]$ (respectively, $r\in (p,\infty )$). $E$ is said to be exactly $\Lambda ^\beta $ (respectively, exactly non-$\Lambda ^\beta $) if $E$ has the property$(**)\hspace{28.45274pt}\text{every} \displaystyle {f\in L^2_E(G) \text{satisfies} \int _G {\rm exp} (\lambda |f|^{2/\alpha }< \infty , \text{for} \text{all} \lambda >0,}$ if and only if $\alpha \in [\beta ,\infty )$ (respectively, $\alpha \in (\beta ,\infty )$).In this paper, for every $p\in [1,2)$ and $\beta \in [1,\infty )$, we display sets which are exactly $p$-Sidon, exactly non-$p$-Sidon, exactly $\Lambda ^\beta $ and exactly non-$\Lambda ^\beta $.
LA - eng
UR - http://eudml.org/doc/74413
ER -