Boundary behavior of holomorphic functions in the ball

Jacob Burbea
1987 Pacific Journal of Mathematics  
A description of the boundary behavior of functions belonging to certain Sobolev classes of holomorphic functions on the unit ball B n of C" is given in terms of bounded and vanishing mean oscillation. In particular, it is shown that the boundary values of any holomorphic function on B n , whose fractional derivative of order n/p belongs to the Hardy class H p (B n ), have vanishing mean oscillation provided 0 < p < 2. JACOB BURBEA Since M p (f: •) is a non-negative increasing function on
more » ... we deduce that for any q > 0 ( 5. 3) ([ J o * J ι/2
doi:10.2140/pjm.1987.127.1 fatcat:4bxcfzqpobagtmd5mfzudfkq6i