Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on the Hardy type inequalities with remainder terms in the
  framework of equalities   We study the Hardy type inequalities in the framework of equalities. We
present equalities which immediately imply Hardy type inequalities by dropping
the remainder term. Simultaneously we give a characterization of the class of
functions which makes the remainder term vanish. A point of our observation is
to apply an orthogonality properties in general Hilbert space, and which gives
a simple and direct understanding of the Hardy type inequalities as well as the
nonexistence of nontrivial extremizers.

28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: eess
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
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The categories of this paper are: supr-con