Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic Calder\'on-Zygmund theory   Calder\'on-Zygmund theory has been traditionally developed on metric measure
spaces satisfying additional regularity properties. In the lack of good
metrics, we introduce a new approach for general measure spaces which admit a
Markov semigroup satisfying purely algebraic assumptions. We shall construct an
abstract form of "Markov metric" governing the Markov process and the naturally
associated BMO spaces, which interpolate with the Lp-scale and admit endpoint
inequalities for Calder\'on-Zygmund operators. Motivated by noncommutative
harmonic analysis, this approach gives the first form of Calder\'on-Zygmund
theory for arbitrary von Neumann algebras, but is also valid in classical
settings like Riemannian manifolds with nonnegative Ricci curvature or
doubling/nondoubling spaces. Other less standard commutative scenarios like
fractals or abstract probability spaces are also included. Among our
applications in the noncommutative setting, we improve recent results for
quantum Euclidean spaces and group von Neumann algebras, respectively linked to
noncommutative geometry and geometric group theory.

1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg