Premium
The norm of the characteristic function of a set in the John‐Nirenberg space of exponent p
Author(s) -
Blasco Oscar,
EspinozaVillalva Carolina
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6124
Subject(s) - mathematics , nirenberg and matthaei experiment , exponent , norm (philosophy) , standard probability space , lebesgue measure , measure (data warehouse) , space (punctuation) , pure mathematics , lebesgue integration , measurable function , mathematical analysis , function (biology) , lp space , discrete mathematics , banach space , philosophy , linguistics , database , evolutionary biology , political science , computer science , law , biology , bounded function
We find the concrete value of ‖ χ A‖J N p ( R )for any measurable set A ⊂ R of positive and finite Lebesgue measure, whereJ N pstands for the John‐Nirenberg space of exponent 1 ≤ p ≤ ∞ . In the caseI 0 = [ 0 , 1 ] we show that ‖ χ I‖J N p ( I 0 ) = 2 ℓ ( 1 − ℓ ) for any interval I ⊂ I 0with | I | = ℓ and any 1 ≤ p ≤ p ℓwherep ℓ = max1 − ℓ ℓ , ℓ 1 − ℓmax1 − ℓ ℓ , ℓ 1 − ℓ− 1 .