Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An $L_q(L_p)$-theory for parabolic pseudo-differential equations:
  Calder\'on-Zygmund approach   In this paper we present a Calder\'{o}n-Zygmund approach for a large class of
parabolic equations with pseudo-differential operators $\mathcal{A}(t)$ of
arbitrary order $\gamma\in(0,\infty)$. It is assumed that $\cA(t)$ is merely
measurable with respect to the time variable. The unique solvability of the
equation $$ \frac{\partial u}{\partial t}=\cA u-\lambda u+f, \quad (t,x)\in
\fR^{d+1} $$
  and the $L_{q}(\fR,L_{p})$-estimate $$
\|u_{t}\|_{L_{q}(\fR,L_{p})}+\|(-\Delta)^{\gamma/2}u\|_{L_{q}(\fR,L_{p})}
+\lambda\|u\|_{L_{q}(\fR,L_{p})}\leq N\|f\|_{L_{q}(\fR,L_{p})} $$ are obtained
for any $\lambda > 0$ and $p,q\in (1,\infty)$.

18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th