Variable Lebesgue norm estimates for BMO functions

Mitsuo Izuki; Yoshihiro Sawano

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 3, page 717-727
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Izuki, Mitsuo, and Sawano, Yoshihiro. "Variable Lebesgue norm estimates for BMO functions." Czechoslovak Mathematical Journal 62.3 (2012): 717-727. <http://eudml.org/doc/246501>.

@article{Izuki2012,
abstract = {In this paper, we are going to characterize the space $\{\rm BMO\}(\{\mathbb \{R\}\}^n)$ through variable Lebesgue spaces and Morrey spaces. There have been many attempts to characterize the space $\{\rm BMO\}(\{\mathbb \{R\}\}^n)$ by using various function spaces. For example, Ho obtained a characterization of $\{\rm BMO\}(\{\mathbb \{R\}\}^n)$ 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.},
author = {Izuki, Mitsuo, Sawano, Yoshihiro},
journal = {Czechoslovak Mathematical Journal},
keywords = {variable exponent; Morrey space; BMO; variable exponent; Morrey space; BMO},
language = {eng},
number = {3},
pages = {717-727},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Variable Lebesgue norm estimates for BMO functions},
url = {http://eudml.org/doc/246501},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Izuki, Mitsuo
AU - Sawano, Yoshihiro
TI - Variable Lebesgue norm estimates for BMO functions
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 3
SP - 717
EP - 727
AB - In this paper, we are going to characterize the space ${\rm BMO}({\mathbb {R}}^n)$ through variable Lebesgue spaces and Morrey spaces. There have been many attempts to characterize the space ${\rm BMO}({\mathbb {R}}^n)$ by using various function spaces. For example, Ho obtained a characterization of ${\rm BMO}({\mathbb {R}}^n)$ 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.
LA - eng
KW - variable exponent; Morrey space; BMO; variable exponent; Morrey space; BMO
UR - http://eudml.org/doc/246501
ER -

References

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