Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Kor\'anyi Spherical maximal function on Heisenberg groups   We prove $L^p\to L^q$ estimates for the local maximal operator associated
with dilates of the K\'oranyi sphere in Heisenberg groups. These estimates are
sharp up to endpoints and imply new bounds on sparse domination for the
corresponding global maximal operator. We also prove sharp $L^p\to L^q$
estimates for spherical means over the Kor\'anyi sphere, which can be used to
improve the sparse domination bounds for the associated lacunary maximal
operator.

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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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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: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn