Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp $L^p$ estimates of powers of the complex Riesz transform   Let $R_{1,2}$ be scalar Riesz transforms on $\mathbb{R}^2$. We prove that the
$L^p$ norms of $k$-th powers of the operator $R_2+iR_1$ behave exactly as
$|k|^{1-2/p}p$, uniformly in $k\in\mathbb{Z}\backslash\{0\}$, $p\geq2$. This
gives a complete asymptotic answer to a question suggested by Iwaniec and
Martin in 1996. The main novelty are the lower estimates, of which we give
three different proofs. We also conjecture the exact value of
$\|(R_2+iR_1)^k\|_p$. Furthermore, we establish the sharp behaviour of weak
$(1,1)$ constants of $(R_2+iR_1)^k$ and an $L^\infty$ to $BMO$ estimate that is
sharp up to a logarithmic factor.

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The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
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The categories of this paper are: eess
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph