Exact location of alpha-Bloch spaces in L-a(p) and H-p of a complex unit ball

In this paper we prove that, on the unit ball of C-n, (i) for f is an eleme nt of H(B) and 0 < <alpha> < <infinity>, f is an element of B-alpha double left right arrow sup(z is an element ofB) \Rf(z)\(1 - \z\(2))(alpha) < <inf inity>; as a corollary, B-alpha = A(B) boolean AND Lip(1 - alpha) for 0 < < alpha> < 1. (ii) B<alpha>(<1+(1/p)) <subset of> L-a(p) subset of B1+((n+1)/ p), B-alpha(<1) <subset of> H-p subset of B1+(n/p) for n > 1 and 0 < p < in finity, where L-a(p), H-p denote the Bergman spaces and Hardy spaces, respe ctively. And B-1 subset of boolean AND L-0<p<infinity(a)P subset of B-alpha (>1), B-alpha(<1) <subset of> boolean AND H-0<p<infinity(p) subset of B-alp ha(>1). Further, it is proved with constructive methods that all of the abo ve containments are strict and best possible.