The Logarithm of the Modulus of an Entire Function as a Minorant for a Subharmonic Function outside a Small Exceptional Set

摘要

Let u 6≡ −∞ be a subharmonic function on the complex plane C. In 2016, we obtained a result on the existence of an entire function f 6= 0 satisfying the estimate log f ≤ Bu on C, where the functions Bu are integral averages of u for rapidly shrinking disks as it approaches infinity. We give another equivalent version of this result with log f ≤ u outside a very small exceptional set if u is of finite order.