Abstract
In this paper, we are going to characterize the space BMO(ℝ n) through variable Lebesgue spaces and Morrey spaces. There have been many attempts to characterize the space BMO(ℝ n) by using various function spaces. For example, Ho obtained a characterization of BMO(ℝ n) with respect to rearrangement invariant spaces. However, variable Lebesgue spaces and Morrey spaces do not appear in the characterization. One of the reasons is that these spaces are not rearrangement invariant. We also obtain an analogue of the well-known John-Nirenberg inequality which can be seen as an extension to the variable Lebesgue spaces.
| Original language | English |
|---|---|
| Pages (from-to) | 717-727 |
| Number of pages | 11 |
| Journal | Czechoslovak Mathematical Journal |
| Volume | 62 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Sep 2012 |
| Externally published | Yes |
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Keywords
- BMO
- Morrey space
- variable exponent
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Variable Lebesgue norm estimates for BMO functions. / Izuki, Mitsuo; Sawano, Yoshihiro.
In: Czechoslovak Mathematical Journal, Vol. 62, No. 3, 09.2012, p. 717-727.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Variable Lebesgue norm estimates for BMO functions
AU - Izuki, Mitsuo
AU - Sawano, Yoshihiro
PY - 2012/9
Y1 - 2012/9
N2 - In this paper, we are going to characterize the space BMO(ℝ n) through variable Lebesgue spaces and Morrey spaces. There have been many attempts to characterize the space BMO(ℝ n) by using various function spaces. For example, Ho obtained a characterization of BMO(ℝ n) with respect to rearrangement invariant spaces. However, variable Lebesgue spaces and Morrey spaces do not appear in the characterization. One of the reasons is that these spaces are not rearrangement invariant. We also obtain an analogue of the well-known John-Nirenberg inequality which can be seen as an extension to the variable Lebesgue spaces.
AB - In this paper, we are going to characterize the space BMO(ℝ n) through variable Lebesgue spaces and Morrey spaces. There have been many attempts to characterize the space BMO(ℝ n) by using various function spaces. For example, Ho obtained a characterization of BMO(ℝ n) with respect to rearrangement invariant spaces. However, variable Lebesgue spaces and Morrey spaces do not appear in the characterization. One of the reasons is that these spaces are not rearrangement invariant. We also obtain an analogue of the well-known John-Nirenberg inequality which can be seen as an extension to the variable Lebesgue spaces.
KW - BMO
KW - Morrey space
KW - variable exponent
UR - http://www.scopus.com/inward/record.url?scp=84867668341&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84867668341&partnerID=8YFLogxK
U2 - 10.1007/s10587-012-0042-5
DO - 10.1007/s10587-012-0042-5
M3 - Article
VL - 62
SP - 717
EP - 727
JO - Czechoslovak Mathematical Journal
JF - Czechoslovak Mathematical Journal
SN - 0011-4642
IS - 3
ER -