BMO-scale of distribution on $\mathbb {R}^n$

Title:

BMO-scale of distribution on $\mathbb {R}^n$

Creator:

Castillo, René Erlín and Fernández, Julio C. Ramos

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:f9bba117-0471-46d0-9efb-f8f6b205b5de
uuid:f9bba117-0471-46d0-9efb-f8f6b205b5de

Subject:

$\mathop {\rm BMO}$, $\mathop {\rm VMO}$, John and Niereberg, and Bessel potential

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 $J^{-\alpha }f\in \mathop {\mathrm BMO}$, then for any $\lambda \in (0,1)$, $J^{-\alpha }(f)_\lambda \in \mathop {\mathrm BMO}$, 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 $\mathop {\mathrm VMO}$ space.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

505-516

Source:

Czechoslovak Mathematical Journal | 2008 Volume:58 | Number:2

Harvested from:

CDK

Metadata only:

false