Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lipschitz free spaces isomorphic to their infinite sums and geometric
  applications   We find general conditions under which Lipschitz-free spaces over metric
spaces are isomorphic to their infinite direct $\ell_1$-sum and exhibit several
applications. As examples of such applications we have that Lipschitz-free
spaces over balls and spheres of the same finite dimensions are isomorphic,
that the Lipschitz-free space over $\mathbb{Z}^d$ is isomorphic to its
$\ell_1$-sum, or that the Lipschitz-free space over any snowflake of a doubling
metric space is isomorphic to $\ell_1$. Moreover, following new ideas from [E.
Bru\`e, S. Di Marino and F. Stra, Linear Lipschitz and $C^1$ extension
operators through random projection, arXiv:1801.07533] we provide an elementary
self-contained proof that Lipschitz-free spaces over doubling metric spaces are
complemented in Lipschitz-free spaces over their superspaces and they have BAP.
Everything, including the results about doubling metric spaces, is explored in
the more comprehensive setting of $p$-Banach spaces, which allows us to
appreciate the similarities and differences of the theory between the cases
$p<1$ and $p=1$.

18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga