Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Riemann-Liouville type operators, BMO, gradient estimates in the
  L\'evy-It\^o space, and approximation   We discuss in a stochastic framework the interplay between Riemann-Liouville
type operators applied to stochastic processes, real interpolation, bounded
mean oscillation, and an approximation problem for stochastic integrals. We
provide upper and lower bounds for gradient processes on the L\'evy-It\^o
space, which arise in the special case of the Wiener space from the Feynman-Kac
theory for parabolic PDEs. The upper bounds are formulated in terms of
BMO-conditions on the fractional integrated gradient, the lower bounds in terms
of oscillatory quantities. On the general L\'evy-It\^o space we are concerned
with gradient processes with values in a Hilbert space, where the regularity
depends on the direction in this Hilbert space. We discuss two applications of
our techniques: on the Wiener space an approximation problem for H\"older
functionals and on the L\'evy-It\^o space an orthogonal decomposition of
H\"older functionals into a sum of stochastic integrals with a control of the
corresponding integrands.

6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
9
The categories of this paper are: nlin
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The categories of this paper are: hep-ex