RT Journal Article
T1 Weighted Lp estimates on the infinite rooted k-ary tree.
A1 Ombrosi, Sheldy J.
A1 Rivera Ríos, Israel P.
K1 Desigualdades (Matemáticas)
AB In this paper sufficient conditions for weighted weak and strong type (p, p) estimates with  for the centered maximal function on the infinite rooted k-ary tree are provided. Here the line initated by the authors and Safe in Ombrosi et al. (Int Math Res Not IMRN 4:2736–2762, 2021) and providing a further extension of the use of techniques due to Naor and Tao in (J Funct Anal 259(3):731–779, 2010) is continued. The fact that the class of weights from the sufficient conditions is wider for  estimates than the one obtained in [16] is established as well. Some results highlighting the pathological nature of the weighted  theory in this setting are settled. It is shown that the  condition is no precise in this setting, since there exist weights such that the  boundedness holds but the  condition is not satisfied. It is also shown that the Sawyer type testing condition is not sufficient either for the strong type to hold and also that strong and weak type estimates are not equivalent in this setting. It will be shown as well that the one weight results can be extended to the two weight setting.
PB Springer Nature
YR 2021
FD 2021
LK https://hdl.handle.net/10630/35572
UL https://hdl.handle.net/10630/35572
LA eng
NO Ombrosi, S., Rivera-Ríos, I.P. Weighted   estimates on the infinite rooted k-ary tree. Math. Ann. 384, 1–20 (2022). https://doi.org/10.1007/s00208-021-02298-0
NO Política de acceso abierto tomada de:https://openpolicyfinder.jisc.ac.uk/id/publication/8105
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 13 abr 2026