Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6418288 | Journal of Mathematical Analysis and Applications | 2014 | 32 Pages |
Let B denote the unit ball in RN with boundary S. For a non-negative C2 subharmonic function f on B and ζâS, we define the Lusin square area integral Sα(ζ,f) bySα(ζ,f)=[â«Îα(ζ)(1â|x|)2âNÎf2(x)dx]12,where for α>1, Îα(ζ)={xâB:|xâζ|<α(1â|x|)} is the non-tangential approach region at ζâS, and Î is the Laplacian in RN. In the paper we will prove the following: Let f be a non-negative subharmonic function such that fpois subharmonic for some po>0. Ifâfâpp=sup0 (2Nâ3)/(Nâ1).