A. Logunov

activity

20132026

most citedOn ratios of harmonic functions

15 citations · 47 across the 16 of their papers we have counts for

collaborators

Showing 2014Show all

3 papers · 1 filter

math.AP2014

On the higher-dimensional harmonic analog of the Levinson log log theorem

Alexander Logunov

Let $M : (0, 1) \to [e, + \infty)$ be a decreasing function such that $0 \int 1 lo g lo g M (y) d y < + \infty$ . Consider the set $H_{M}$ of all functions $u$ harmonic in $P:=\{(…

math.CA2014

On a theorem of M. Cartwright in higher dimensions

A. Logunov, E. Malinnikova, P. Mozolyako

We consider harmonic functions in the unit ball of $R^{n + 1}$ that are unbounded near the boundary but can be estimated from above by some (rapidly increasing) radial weigh…

math.AP2014★ 15 cited

On ratios of harmonic functions

Alexander Logunov, Eugenia Malinnikova

Let $u$ and $v$ be harmonic in $Ω \subset R^{n}$ functions with the same zero set $Z$ . We show that the ratio $f$ of such functions is always well-defined and is real analyt…