Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partial derivatives, singular integrals and Sobolev Spaces in dyadic
  settings   In this note we show that the general theory of vector valued singular
integral operators of Calder\'on-Zygmund defined on general metric measure
spaces, can be applied to obtain Sobolev type regularity properties for
solutions of the dyadic fractional Laplacian. In doing so, we define partial
derivatives in terms of Haar multipliers and dyadic homogeneous singular
integral operators.

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The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int