Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal operators of exotic and non-exotic Laguerre and other semigroups
  associated with classical orthogonal expansions   Classical settings of discrete and continuous orthogonal expansions, like
Laguerre, Bessel and Jacobi, are associated with second order differential
operators playing the role of the Laplacian. These depend on certain parameters
of type that are usually restricted to a half-line, or a product of half-lines
if higher dimensions are considered. Following earlier research done by
Hajmirzaahmad, we deal in this paper with Laplacians in the above-mentioned
contexts with no restrictions on the type parameters and bring to attention
naturally associated orthogonal systems that in fact involve the classical
ones, but are different. This reveals new frameworks related to classical
orthogonal expansions and thus new potentially rich research areas, at least
from the harmonic analysis perspective. To support the last claim we focus on
maximal operators of multi-dimensional Laguerre, Bessel and Jacobi semigroups,
with unrestricted type parameters, and prove that they satisfy weak type (1,1)
estimates with respect to the appropriate measures. Generally, these measures
are not (locally) finite, which makes a contrast with the classical situations
and generates new difficulties. An important partial result of the paper is a
new proof of the weak type (1,1) estimate for the classical multi-dimensional
Laguerre semigroup maximal operator.

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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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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: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph