Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Abel summability of Jacobi polynomials series, the Watson Kernel and
  applications   In this paper we return to the study of the Watson kernel for the Abel
summabilty of Jacobi polynomial series. These estimates have been studied for
over more than 30 years. The main innovations are in the techniques used to get
the estimates that allow us to handle the case 0<\alpha as well as -1< \alpha
<0, with essentially the same method; using an integral superposition of
Poisson type kernel and Muckenhoupt A_p-weight theory. We consider a
generalization of a theorem due to Zygmund in the context to Borel measures.
The proofs are therefore different from the ones given in previous papers by
several authors. We will also discuss in detail the Calder\'on-Zygmund
decomposition for non-atomic Borel measures in the real line. Then, we prove
that the Jacobi measure is doubling and therefore, following a work of A. P.
Calder\'on, we study the corresponding A_p weight theory in the setting of
Jacobi expansions, considering power weights of the form (1-x)^{\bar{\alpha}},
(1+x)^{\bar{\beta}}, -1 < {\bar{\alpha}}<0,\, -1 < {\bar{\beta}}<0 with
negative exponents. Finally, as an application of the weight theory we obtain
L^p estimates for the maximal operator of Abel summability of Jacobi function
expansions for suitable values of p.

3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph