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

1988; Wiley; Volume: 20; Issue: 1 Linguagem: Inglês

10.1112/blms/20.1.73

1469-2120

Ryszard A. Komorowski,

Mathematical Approximation and Integration

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 2 where C ( p , n ) = ( ∫ 0 1 | ∑ i − 1 n r i | p d t ) 1 / p n 1 2 . This gives stronger estimates than the hitherto Known ones for the constants depend on n.