The norm of the characteristic function of a set in the John‐Nirenberg space of exponent   p | Zendy

Blasco Oscar | Zendy; EspinozaVillalva Carolina | Zendy

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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 .

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