TY - JOUR
T1 - On Function Spaces with Mixed Norms — A Survey
AU - Huang , Long
AU - Yang , Dachun
JO - Journal of Mathematical Study
VL - 3
SP - 262
EP - 336
PY - 2021
DA - 2021/03
SN - 54
DO - http://doi.org/10.4208/jms.v54n3.21.03
UR - https://global-sci.org/intro/article_detail/jms/18735.html
KW - Mixed norm, (weak) Lebesgue space, Morrey space, Hardy space, maximal function,
Littlewood–Paley function, Calderón–Zygmund operator.
AB - <p style="text-align: justify;">The targets of this article are threefold. The first one is to give a survey on the
recent developments of function spaces with mixed norms, including mixed Lebesgue
spaces, iterated weak Lebesgue spaces, weak mixed-norm Lebesgue spaces and mixed
Morrey spaces as well as anisotropic mixed-norm Hardy spaces. The second one is
to provide a detailed proof for a useful inequality about mixed Lebesgue norms and
the Hardy–Littlewood maximal operator and also to improve some known results on
the maximal function characterizations of anisotropic mixed-norm Hardy spaces and
the boundedness of Calderón–Zygmund operators from these anisotropic mixed-norm Hardy spaces to themselves or to mixed Lebesgue spaces. The last one is to correct
some errors and seal some gaps existing in the known articles.</p>