TY - JOUR
T1 - On 2-Microlocal Herz Type Besov and Triebel-Lizorkin Spaces with Variable Exponents
AU - Fang , Chenglong
AU - Zhou , Jiang
JO - Journal of Mathematical Study
VL - 3
SP - 227
EP - 249
PY - 2021
DA - 2021/03
SN - 54
DO - http://doi.org/10.4208/jms.v54n3.21.01
UR - https://global-sci.org/intro/article_detail/jms/18733.html
KW - 2-microlocal, variable exponent, Herz type spaces, Besov spaces, Triebel-Lizorkin
spaces, Peetre's maximal operator.
AB - <p style="text-align: justify;">In this paper, 2-microlocal Herz type Besov and Triebel-Lizorkin spaces with
variable exponents are introduced for the first time. Then, we give characterizations of
these spaces by so-called Peetre&#39;s maximal functions. Further, the atomic and molecular decompositions of these spaces are obtained. Finally, using the characterizations of
the spaces by local means and molecular decomposition we obtain the wavelet characterizations.</p>