| Title:
|
BMO-scale of distribution on $\mathbb {R}^n$ (English) |
| Author:
|
Castillo, René Erlín |
| Author:
|
Fernández, Julio C. Ramos |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
505-516 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
$\mathop {\rm BMO}$ |
| Keyword:
|
$\mathop {\rm VMO}$ |
| Keyword:
|
John and Niereberg |
| Keyword:
|
Bessel potential |
| MSC:
|
32A37 |
| MSC:
|
46E30 |
| MSC:
|
46F05 |
| idZBL:
|
Zbl 1171.46310 |
| idMR:
|
MR2411106 |
| . |
| Date available:
|
2009-09-24T11:56:35Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128274 |
| . |
| Reference:
|
[1] F. John and L. Nirenberg: On functions of bounded mean oscillation.Comm. Pure Appl. Math. 14 (1961), 415–426. MR 0131498, 10.1002/cpa.3160140317 |
| Reference:
|
[2] D. Sarason: Functions of bounded mean oscillation.Trans. Amer. Math. Soc. 201 (1975), 391–405. MR 0377518 |
| Reference:
|
[3] E. M. Stein: Singular Integrals and Differentiability Properties of Functions.Princenton University Press, Princenton, NJ, 1970. Zbl 0207.13501, MR 0290095 |
| Reference:
|
[4] W. R. Wade: An introduction to Analysis, 2nd ed.Prentice Hall, NJ, 2000. Zbl 0951.26001 |
| . |
