Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Riesz transforms, Cauchy-Riemann systems and amalgam Hardy spaces   In this paper we study Hardy spaces $\mathcal{H}^{p,q}(\mathbb{R}^d)$,
$0<p,q<\infty$, modeled over amalgam spaces $(L^p,\ell^q)(\mathbb{R}^d)$. We
characterize $\mathcal{H}^{p,q}(\mathbb{R}^d)$ by using first order classical
Riesz transforms and compositions of first order Riesz transforms depending on
the values of the exponents $p$ and $q$. Also, we describe the distributions in
$\mathcal{H}^{p,q}(\mathbb{R}^d)$ as the boundary values of solutions of
harmonic and caloric Cauchy-Riemann systems. We remark that caloric
Cauchy-Riemann systems involve fractional derivative in the time variable.
Finally we characterize the functions in $L^2(\mathbb{R}^d) \cap
\mathcal{H}^{p,q}(\mathbb{R}^d)$ by means of Fourier multipliers $m_\theta$
with symbol $\theta(\cdot/|\cdot|)$, where $\theta \in
C^\infty(\mathbb{S}^{d-1})$ and $\mathbb{S}^{d-1}$ denotes the unit sphere in
$\mathbb{R}^d$.

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The categories of this paper are: physics
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
18
The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph