Some characterizations of BLO space | Zendy

Wang Dinghuai | Zendy; Zhou Jiang | Zendy; Teng Zhidong | Zendy

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Some characterizations of BLO space

Author(s) -

Wang Dinghuai,

Zhou Jiang,

Teng Zhidong

Publication year - 2018

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201700318

Subject(s) - mathematics , lp space , corollary , norm (philosophy) , function space , space (punctuation) , lebesgue's number lemma , lebesgue integration , pure mathematics , standard probability space , discrete mathematics , riemann integral , banach space , operator theory , computer science , epistemology , philosophy , fourier integral operator , operating system

For 0 < p < ∞ , a real‐valued function f ∈ L loc 1belongs to B L O pspace if∥ f ∥B L O p : = sup Q1 | Q |∫ Qf ( x ) − essinf y ∈ Q f ( y )p d x1 / p < ∞ . In this paper, we establish a version of John–Nirenberg inequality suitable for the B L O pspace with 0 < p ≤ 1 . As a corollary, it is proved thatB L O p spaces are independent of the scale p ∈ ( 0 , ∞ ) in sense of norm. Also, we characterize the space B L O through weighted Lebesgue spaces and variable Lebesgue spaces, respectively.

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