Besov Spaces and Outer Functions

摘要

Let D denote the unit disk {z ∈ C : |z| ＜1}, T its boundary, and m the normal- ized Lebesgue measure on T. For a function f ∈ L~P (:= L~P(T, m)), we define its L~P modulus of continuity by Formula (ell) For 0 ≤ t ≤π, and by ω_P(t, f):=ω_P(π, f) for π＜t＜∞. Further, given 1＜s＜1, 0＜p＜∞, and 0＜q＜∞, the Besov space B~s_pq= B~s_pq(T) is introduced as follows: ............a formula (ell.)...............