Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Composition operators and embedding theorems for some function spaces of
  Dirichlet series   We observe that local embedding problems for certain Hardy and Bergman spaces
of Dirichlet series are equivalent to boundedness of a class of composition
operators. Following this, we perform a careful study of such composition
operators generated by polynomial symbols $\varphi$ on a scale of Bergman--type
Hilbert spaces $\mathcal{D}_\alpha$. We investigate the optimal $\beta$ such
that the composition operator $\mathcal{C}_\varphi$ maps $\mathcal{D}_\alpha$
boundedly into $\mathcal{D}_\beta$. We also prove a new embedding theorem for
the non-Hilbertian Hardy space $\mathcal H^p$ into a Bergman space in the
half-plane and use it to consider composition operators generated by polynomial
symbols on $\mathcal{H}^p$, finding the first non-trivial results of this type.
The embedding also yields a new result for the functional associated to the
multiplicative Hilbert matrix.

12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
9
The categories of this paper are: nlin