ABSTRACT
Composition Operators as Integral Operators 549
0Kb( • ,e 1 t>ll 1
< 1 for all
550 Sarason
that lbl < 1 almost everywhere on oD. (For, if the condition fails, then the sequence ( bl'l) 00 1 does not tend to 0
Composition Operators as Integral Operators 551
552 Sarason
Composition Operators as Integral Operators 553
compactness of on implies its compactness on If. The reverse implication would be surprising, but I have been
554 Sarason
of H00 that vanishes at the origin. I do not have an ex-
Composition Operators as Integral Operators 555
obviously compact on M and maps M into Ll, so it will
556 Sarason
+-he measure ~ Rb{e 18 ,e1 t.) de. Since Cbot is a probability 1 d +h +- IlK.( ,eit)ll 1 = 1, i.e., measure, we can cone u e . a . -~ •
IV. A SUFFICIENT CONDITION FOR COMPACTNESS ON 11
on ~.
