Variable Lebesgue norm estimates for BMO functions

Mitsuo Izuki; Yoshihiro Sawano

doi:10.1007/s10587-012-0042-5

Variable Lebesgue norm estimates for BMO functions

Mitsuo Izuki, Yoshihiro Sawano

Graduate School of Education

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

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	https://doi.org/10.1007/s10587-012-0042-5
Publication status	Published - Sep 2012

Keywords

BMO
Morrey space
variable exponent

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s10587-012-0042-5

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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.",

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AU - Izuki, Mitsuo

AU - Sawano, Yoshihiro

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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.

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KW - Morrey space

KW - variable exponent

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Variable Lebesgue norm estimates for BMO functions

Abstract

Keywords

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