Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subordination by orthogonal martingales in $L^{p}$ and zeros of Laguerre
  polynomials   In this paper we address the question of finding the best $L^p$-norm constant
for martingale transforms with one-sided orthogonality. We consider two
martingales on a probability space with filtration $\mathcal{B}$ generated by a
two-dimensional Brownian motion $B_t$. One is differentially subordinated to
the other. Here we find the sharp estimate for subordinate martingales if the
subordinated martingale is orthogonal and $1<p<2$, and we find the best
constant if $p>2$, but the orthogonal martingale is a subordinator. The answers
are given in terms of zeros of Laguerre polynomials. As an application of our
sharp constant we obtain a new estimate for the norm of theAhlfors--Beurling
operator. We estimate it as $1.3922(p-1)$ asymptotically for large $p$.

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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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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: cs
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: econ