Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Essential norms and weak compactness of integral operators between
  weighted Bergman spaces   We consider Volterra-type integration operators $T_g$ between Bergman spaces
induced by weights $\omega$ satisfying a doubling property. We derive estimates
for the operator norms, essential and weak essential norms of $T_g: A_\omega^p
\to A_\omega^q$, $0<p\leq q<\infty$. In particular, the operator $T_g:
A_\omega^1\to A_\omega^1$ is weakly compact if and only if it is compact.

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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph