Fractional derivatives of holomorphic functions on bounded symmetric domains of C

Let f∈H(Bn). f|β| denotes the βth fractional derivative of f. If f|β|∈Ap,q,α(Bn), we show tha

Extensions of Hardy-Littlewood inequalities

For a function f∈Hp(Bn), with f(0)=0, we prov

Generalizations of inequalities of littlewood and paley

For a function f, holomorphic in the open unit ball Bn in Cn, with f(0)=0, we prove (I) If 0<s≤2 and s≤p<∞ Then ‖f‖pp≤C∫01∫∂Bn|f(ρζ)|p−s|Rf(ρζ)|s(log1/ρ)s−1ρ−1dσ(ζ)dρ (ii) If 2≤B≤p<∞ Then ∫01∫∂Bn|f(ρζ)|p−s|Rf(ρζ)|s(log1/ρ)s−1ρ−1dσ(ζ)dρ≤C‖f‖pp where Rf is the radial dervative of f, generalizing the known cases p=s([1]) and p=s, n=1 ([2])