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SUMMARY:The Nevanlinna characteristic and integral inequalities with maxim
al radial characteristic for meromorphic functions and differences of subh
armonic functions
DTSTART;VALUE=DATE-TIME:20210704T070000Z
DTEND;VALUE=DATE-TIME:20210704T074000Z
DTSTAMP;VALUE=DATE-TIME:20240525T104843Z
UID:indico-contribution-191@indico.eimi.ru
DESCRIPTION:Speakers: Bulat Khabibullin (Bashkir State University)\nLet $f
$ be a meromorphic function on the complex plane $\\mathbb C$ with the max
imum function of its modulus $M(r\,f)$ on circles centered at zero of radi
us $r$. A number of classical\, well-known and widely used results allow u
s to estimate from above the integrals of the positive part of the logarit
hm ln M(t\,f) over subsets of $E\\subset [0\,r]$ via the Nevanlinna charac
teristic T(r\,f) and the linear Lebesgue measure of the set $E$. We give m
uch more general estimates for the Lebesgue-Stieltjes integrals of $ln^+M(
t\,f)$ over the increasing integration function of $m$. Our results are es
tablished immediately for the differences of subharmonic functions on clos
ed circles centered at zero\, i.e.\, $ \\delta $ -subharmonic functions\,
but they are new for meromorphic functions on $\\mathbb C$ and contain all
the previous results on this topic as a very special and extreme case. Th
e only condition in our main theorem is the Dini condition for the modulus
of continuity of the integration function $m$. This condition is\, in a s
ense\, necessary. Thus\, our results\, to a certain extent\, complete stud
y upper estimates of the integrals of the radial maximum growth characteri
stics of arbitrary meromorphic and $\\delta$-subharmonic functions through
the Nevanlinna characteristic with its versions and through quantities a
ssociated with the integration function $m$ such as the Hausdorff $h$-mea
sure or $h$-content\, and the $d$-dimensional Hausdorff measure of the sup
port of nonconstancy for $m$.\n\nhttps://indico.eimi.ru/event/321/contribu
tions/191/
LOCATION:
URL:https://indico.eimi.ru/event/321/contributions/191/
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