Generalizations of inequalities of littlewood and paley

Lou Zengjian

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-3

Abstract:

For a function f , holomorphic in the open unit ball B n in C n , with f ( 0 ) = 0 , we prove (I) If 0 < s ≤ 2 and s ≤ p < ∞ Then ‖ f ‖ p p ≤ C ∫ 0 1 ∫ ∂ B n | f ( ρ ζ ) | p − s | R f ( ρ ζ ) | s ( log 1 / ρ ) s − 1 ρ − 1 d σ ( ζ ) d ρ (ii) If 2 ≤ B ≤ p < ∞ Then ∫ 0 1 ∫ ∂ B n | f ( ρ ζ ) | p − s | R f ( ρ ζ ) | s ( log 1 / ρ ) s − 1 ρ − 1 d σ ( ζ ) d ρ ≤ C ‖ f ‖ p p where R f is the radial dervative of f , generalizing the known cases p = s ( [ 1 ] ) and p = s , n = 1 ([2]).

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:540198

DOI: 10.1155/S0161171293000250

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