Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Progress on Hardy-type Inequalities   This paper surveys some of our recent progress on Hardy-type inequa\-lities
which consist of a well-known topic in Harmonic Analysis. In the first section,
we recall the original probabilistic motivation dealing with the stability
speed in terms of the $L^2$-theory. A crucial application of a result by
Fukushima and Uemura (2003) is included. In the second section, the non-linear
case (a general Hardy-type inequality) is handled with a direct and analytic
proof. In the last section, it is illustrated that the basic estimates
presented in the first two sections can still be improved considerably.

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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol