Some remarks on the corona theorem

Sergei Kislyakov
PDMI RAS, Saint Petersburg, Russia

Date(s) : 18/05/2015   iCal
10 h 00 min - 11 h 00 min

With the help of a fixed point theorem, in 1 it is shown that the so-called L-infinity- and L-p-corona problems are equivalent in the general situation. This equivalence extends to the case where L-p is replaced by a more or less arbitrary Banach lattice of measurable functions on the circle. In 2, the corona theorem for l(2)-valued analytic functions is exploited to give a new proof for the existence of an analytic partition of unity subordinate to a weight with logarithm in BMO. In 3, simple observations are presented that make it possible to pass from one sequence space to another in L-infinity-estimates for solutions of corona problems.


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