On the Best Possible Constants in the Khintchine Inequality for  P  ⩾ 3 | Zendy

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On the Best Possible Constants in the Khintchine Inequality for P ⩾ 3

Author(s) -

Komorowski Ryszard

Publication year - 1988

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/20.1.73

Subject(s) - mathematics , constant (computer programming) , combinatorics , inequality , mathematical analysis , computer science , programming language

In the paper the best constants in the Khintchine inequality for p ⩾ 3 are found, namely( ∑ i = 1 n χ i 2 )1 2⩽ ( ∫ 0 1| ∑ i = 1 n χ i r i | p d t ) 1 / p ⩽ C ( p , n ) ( ∑ i = 1 n χ i 2 )1 2where C ( p , n ) =( ∫ 0 1| ∑ i − 1 n r i | p d t ) 1 / pn 1 2.This gives stronger estimates than the hitherto Known ones for the constants depend on n .

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