TY - JOUR
T1 - Discrete Harmonic Analysis Associated with Ultraspherical Expansions
AU - Betancor, Jorge J.
AU - Castro Castilla, Alejandro J.
AU - Fariña, Juan C.
AU - Rodríguez-Mesa, L.
PY - 2020
Y1 - 2020
N2 -
In this paper we study discrete harmonic analysis associated with ultraspherical orthogonal functions. We establish weighted l
p
-boundedness properties of maximal operators and Littlewood-Paley g-functions defined by Poisson and heat semigroups generated by the difference operator ??f(n):=an?f(n+1)-2f(n)+an-1?f(n-1),n?N,?>0,where an?:={(2?+n)(n+1)/[(n+?)(n+1+?)]}1/2, n? N, and a-1?:=0. We also prove weighted l
p
-boundedness properties of transplantation operators associated with the system {fn?}n?N of ultraspherical functions, a family of eigenfunctions of ?
?
. In order to show our results we previously establish a vector-valued local Calderón-Zygmund theorem in our discrete setting.
AB -
In this paper we study discrete harmonic analysis associated with ultraspherical orthogonal functions. We establish weighted l
p
-boundedness properties of maximal operators and Littlewood-Paley g-functions defined by Poisson and heat semigroups generated by the difference operator ??f(n):=an?f(n+1)-2f(n)+an-1?f(n-1),n?N,?>0,where an?:={(2?+n)(n+1)/[(n+?)(n+1+?)]}1/2, n? N, and a-1?:=0. We also prove weighted l
p
-boundedness properties of transplantation operators associated with the system {fn?}n?N of ultraspherical functions, a family of eigenfunctions of ?
?
. In order to show our results we previously establish a vector-valued local Calderón-Zygmund theorem in our discrete setting.
KW - Calderón-Zygmund
KW - Littlewood-Paley functions
KW - Maximal operators
KW - Transplantation operators
KW - Ultraspherical functions
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U2 - 10.1007/s11118-019-09777-9
DO - 10.1007/s11118-019-09777-9
M3 - Article
AN - SCOPUS:85064825727
VL - 53
SP - 523
EP - 563
JO - Potential Analysis
JF - Potential Analysis
SN - 0926-2601
IS - 2
ER -