Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operator Valued Hardy Spaces   We give a systematic study on the Hardy spaces of functions with values in
the non-commutative $L^p$-spaces associated with a semifinite von Neumann
algebra ${\cal}M.$ This is motivated by the works on matrix valued Harmonic
Analysis (operator weighted norm inequalities, operator Hilbert transform), and
on the other hand, by the recent development on the non-commutative martingale
inequalities. Our non-commutative Hardy spaces are defined by the
non-commutative Lusin integral function.

22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom