GENERALIZATIONS OF INEQUALITIES OF LITTLEWOOD AND PALEY

LOU ZENGJIAN

《International Journal of Mathematics and Mathematical Sciences》 1993卷 (1993/12) Pp. 205-207

https://doi.org/10.1155/S0161171293000250

摘要

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(ρζ)|^(p-s)|Rf(ρζ)|^s (log1/ρ)^(s-1) ρ^(-1) dσ(ζ)dρ (ii) If 2≤B≤p＜∞. Then ∫_0^1 ∫_(∂B_n) |f(ρζ)|^(p-s)|Rf(ρζ)|^s (log1/ρ)^(s-1) ρ^(-1) dσ(ζ)dρ ≤ C‖f‖_p^p where Rf is the radial dervative of f, generalizing the known caeses p=s([1]) and p=s, n=1 ([2]).

關鍵字

Radial derivative ； slice function