Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gagliardo-Nirenberg Inequality for rearrangement-invariant Banach
  function spaces   The classical Gagliardo-Nirenberg interpolation inequality is a well-known
estimate which gives, in particular, an estimate for the Lebesgue norm of
intermediate derivatives of functions in Sobolev spaces. We present an
extension of this estimate into the scale of the general
rearrangement-invariant Banach function spaces with the proof based on the
Maz'ya's pointwise estimates. As corollaries, we present the
Gagliardo--Nirenberg inequality for intermediate derivatives in the case of
triples of Orlicz spaces and triples of Lorentz spaces. Finally, we promote the
scaling argument to validate the optimality of the Gagliardo-Nirenberg
inequality and show that the presented estimate in Orlicz scale is optimal.

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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys