Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sobolev inequalities on product Sierpinski spaces   On fractals, different measures (mutually singular in general) are involved
to measure volumes of sets and energies of functions. Singularity of measures
brings difficulties in (especially non-linear) analysis on fractals. In this
paper, we prove a type of Sobolev inequalities, which involve different and
possibly mutually singular measures, on product Sierpinski spaces. Sufficient
and necessary conditions for the validity of these Sobolev inequalities are
given. Furthermore, we compute the sharp exponents which appears in the
sufficient and necessary conditions for the product Kusuoka measure, i.e. the
reference energy measure on Sierpinski spaces.

28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex