Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Directed porosity on conformal iterated function systems and weak
  convergence of singular integrals   The aim of the present paper is twofold. We study directed porosity in
connection with conformal iterated function systems (CIFS) and with singular
integrals. We prove that limit sets of finite CIFS are porous in a stronger
sense than already known. Furthermore we use directed porosity to establish
that truncated singular integral operators, with respect to general Radon
measures $\mu$ and kernels $K$, converge weakly in some dense subspaces of
$L^2(\mu)$ when the support of $\mu$ belongs to a broad family of sets. This
class contains many fractal sets like CIFS's limit sets.

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The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ