Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noncommutative maximal operators with rough kernels   This paper is devoted to the study of noncommutative maximal operators with
rough kernels. More precisely, we prove the weak type $(1,1)$ boundedness for
noncommutative maximal operator with a rough kernel. Then, via the
noncommutative Marcinkiewicz type interpolation theorem, together with a
trivial $(\infty,\infty)$ estimate, we obtain its $L_p$ boundedness for all
$1<p<\infty$. The proof of weak type (1,1) estimate is based on the
noncommutative Calder\'on-Zygmund decomposition. To deal with the rough kernel,
we use the microlocal decomposition in the proofs of both bad and good
functions.

35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an