Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tur\'an-Er\H{o}d type converse Markov inequalities on general convex
  domains of the plane in $\boldsymbol{L^q}$   In 1939 P. Tur\'an started to derive lower estimations on the norm of the
derivatives of polynomials of (maximum) norm 1 on $I:=[-1,1]$ (interval) and
$D:=\{z\in\mathbb{C}~:~|z|\le 1\}$ (disk), under the normalization condition
that the zeroes of the polynomial in question all lie in $I$ or $D$,
respectively. For the maximum norm he found that with $n:=\mathop{\mathrm{deg}}
p$ tending to infinity, the precise growth order of the minimal possible
derivative norm is $\sqrt{n}$ for $I$ and $n$ for $D$.
  J. Er\H{o}d continued the work of Tur\'an considering other domains. Finally,
a decade ago the growth of the minimal possible $\infty$-norm of the derivative
was proved to be of order $n$ for all compact convex domains.
  Although Tur\'an himself gave comments about the above oscillation question
in $L^q$ norms, till recently results were known only for $D$ and $I$.
Recently, we have found order $n$ lower estimations for several general classes
of compact convex domains, and conjectured that even for arbitrary convex
domains the growth order of this quantity should be $n$. Now we prove that in
$L^q$ norm the oscillation order is at least $n/\log n$ for all compact convex
domains.

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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga