@article{Li2022, 
author = {Nan Li},
title = {Summability in anisotropic mixed-norm Hardy spaces},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {9},
pages = {3362-3376},
keywords = {mixed-norm Hardy space, expansive matrix, θ-summability, maximal operator},
url = {https://www.sciopen.com/article/10.3934/era.2022171},
doi = {10.3934/era.2022171},
abstract = {Let        H    A                            p          →                      (            R        n    ) be the anisotropic mixed-norm Hardy space, where              p      →        ∈  (  0  ,  ∞      )    n   and    A is a general expansive matrix on              R        n  . In this paper, a general summability method, the so-called    θ-summability is considered for multi-dimensional Fourier transforms in        H    A                            p          →                      (            R        n    ). Precisely, the author establishes the boundedness of maximal operators, induced by the so-called    θ-means, from        H    A                            p          →                      (            R        n    ) to the mixed-norm Lebesgue space        L                            p          →                      (            R        n    ). As applications, some norm and almost everywhere convergence results of the    θ-means are presented. Finally, the corresponding conclusions of two well-known specific summability methods, namely, Bochner–Riesz and Weierstrass means, are also obtained.}
}