TY - JOUR
T1 - Sparse Non-Smooth Atomic Decomposition of Quasi-Banach Lattices
AU - Hatano, Naoya
AU - Kawasumi, Ryota
AU - Sawano, Yoshihiro
N1 - Funding Information:
Yoshihiro Sawano was supported by Grant-in-Aid for Scientific Research (C) (19K03546), the Japan Society for the Promotion of Science and People’s Friendship University of Russia.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/8
Y1 - 2022/8
N2 - A theory of non-smooth atomic decomposition is obtained for a large class of quasi-Banach lattices, including Morrey spaces, Lorentz spaces, mixed Lebesgue spaces as well as some related function spaces. As an application, an inequality comparing the fractional maximal operator and the fractional integral operator is considered. Some examples show that the restriction posed on quasi-Banach lattices are indispensable. This paper, which is a follow-up of the third author’s paper in 2020, simplifies the proof of some existing results.
AB - A theory of non-smooth atomic decomposition is obtained for a large class of quasi-Banach lattices, including Morrey spaces, Lorentz spaces, mixed Lebesgue spaces as well as some related function spaces. As an application, an inequality comparing the fractional maximal operator and the fractional integral operator is considered. Some examples show that the restriction posed on quasi-Banach lattices are indispensable. This paper, which is a follow-up of the third author’s paper in 2020, simplifies the proof of some existing results.
KW - Decomposition
KW - Fractional integral operators
KW - Quasi-Banach lattices
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U2 - 10.1007/s00041-022-09956-0
DO - 10.1007/s00041-022-09956-0
M3 - Article
AN - SCOPUS:85133438204
SN - 1069-5869
VL - 28
JO - Journal of Fourier Analysis and Applications
JF - Journal of Fourier Analysis and Applications
IS - 4
M1 - 61
ER -