On Bloch-Type Functions with Hadamard Gaps

Stevo Stevic
2007 Abstract and Applied Analysis  
We give some sufficient and necessary conditions for an analytic functionfon the unit ballBwith Hadamard gaps, that is, forf(z)=∑k=1∞Pnk(z)(the homogeneous polynomial expansion off) satisfyingnk+1/nk≥λ>1for allk∈ℕ, to belong to the spaceℬpα(B)={f|sup0<r<1(1−r2)α\|ℛfr\|p<∞,f∈H(B)},p=1,2,∞as well as to the corresponding little space. A remark on analytic functions with Hadamard gaps on mixed norm space on the unit disk is also given.
doi:10.1155/2007/39176 fatcat:bl2j2rghevhjzglj3lcrvhccly