Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some examples of equivalent rearrangement-invariant quasi-norms defined
  via f* or f**   We consider Lorentz-Karamata spaces, small and grand Lorentz-Karamata spaces,
and the so-called $\mathcal{L}$, $\mathcal{R}$, $\mathcal{LL}$, $\mathcal{RL}$,
$\mathcal{RL}$, and $\mathcal{RR}$ spaces. The quasi-norms for a function $f$
in each of these spaces can be defined via the non-increasing rearrangement
$f^*$ or via the maximal function $f^{**}$. We investigate when these
quasi-norms are equivalent. Most of the proofs are based on Hardy-type
inequalities. As application we demonstrate how our general results can be used
to establish interpolation formulae for the grand and small Lorentz-Karamata
spaces.

11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio