Extensions of Hardy-Littlewood inequalities

Zengjian Lou

International Journal of Mathematics and Mathematical Sciences, 1994, vol. 17, 1-3

Abstract:

For a function f ∈ H p ( B n ) , with f ( 0 ) = 0 , we prove

(1) If 0 < p ≤ s ,then ∫ 0 1 r − 1 ( log 1 r ) s β − 1 M p s ( r , R β f ) d r ≤ ‖ f ‖ p s − p ‖ f ‖ p , s , β p (2) If s ≤ p < ∞ , then ‖ f ‖ p , s , β p ≤ ‖ f ‖ p p − s ∫ 0 1 r − 1 ( log 1 r ) s β − 1 M p s ( r , R β f ) d r where R β f is the fractional derivative of f . These results generalize the known cases s = 2 , β = 1 ([1]).

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:679145

DOI: 10.1155/S016117129400027X

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