BMO-scale of distribution on ${ℝ}^n$

Castillo, René Erlín, and Fernández, Julio C. Ramos. "BMO-scale of distribution on $\mathbb {R}^n$." Czechoslovak Mathematical Journal 58.2 (2008): 505-516. <http://eudml.org/doc/31226>.

@article{Castillo2008,
abstract = {Let $S^\{\prime \}$ be the class of tempered distributions. For $f\in S^\{\prime \}$ we denote by $J^\{-\alpha \}f$ the Bessel potential of $f$ of order $\alpha $. We prove that if $J^\{-\alpha \}f\in \mathop \{\mathrm \{B\}MO\}$, then for any $\lambda \in (0,1)$, $J^\{-\alpha \}(f)_\lambda \in \mathop \{\mathrm \{B\}MO\}$, where $(f)_\lambda =\lambda ^\{-n\}f(\phi (\lambda ^\{-1\}\cdot ))$, $\phi \in S$. Also, we give necessary and sufficient conditions in order that the Bessel potential of a tempered distribution of order $\alpha >0$ belongs to the $\mathop \{\mathrm \{V\}MO\}$ space.},
author = {Castillo, René Erlín, Fernández, Julio C. Ramos},
journal = {Czechoslovak Mathematical Journal},
keywords = {$\mathop \{\rm BMO\}$; $\mathop \{\rm VMO\}$; John and Niereberg; Bessel potential; Bessel potential},
language = {eng},
number = {2},
pages = {505-516},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {BMO-scale of distribution on $\mathbb \{R\}^n$},
url = {http://eudml.org/doc/31226},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Castillo, René Erlín
AU - Fernández, Julio C. Ramos
TI - BMO-scale of distribution on $\mathbb {R}^n$
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 2
SP - 505
EP - 516
AB - Let $S^{\prime }$ be the class of tempered distributions. For $f\in S^{\prime }$ we denote by $J^{-\alpha }f$ the Bessel potential of $f$ of order $\alpha $. We prove that if $J^{-\alpha }f\in \mathop {\mathrm {B}MO}$, then for any $\lambda \in (0,1)$, $J^{-\alpha }(f)_\lambda \in \mathop {\mathrm {B}MO}$, where $(f)_\lambda =\lambda ^{-n}f(\phi (\lambda ^{-1}\cdot ))$, $\phi \in S$. Also, we give necessary and sufficient conditions in order that the Bessel potential of a tempered distribution of order $\alpha >0$ belongs to the $\mathop {\mathrm {V}MO}$ space.
LA - eng
KW - $\mathop {\rm BMO}$; $\mathop {\rm VMO}$; John and Niereberg; Bessel potential; Bessel potential
UR - http://eudml.org/doc/31226
ER -