TY - JOUR
T1 - Fractional Operators on Morrey—Lorentz Spaces and the Olsen Inequality
AU - Hatano, N.
N1 - Funding Information:
The author would like to thank Professor Yoshihiro Sawano, in Tokyo Metropolitan University, for his many kinds of ideas and helpful discussion of many questions. In particular, he gave a useful hint with regard to Theorems 4 and 7.
Publisher Copyright:
© 2020, Pleiades Publishing, Ltd.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - Under the Morrey norm, the fractional integral operator and the fractional maximal operator behave similarly as was initially proved by Adams and Xiao. Later on, Tanaka extended this result. The goal of this note is to extend their results on Morrey–Lorentz norm for exponents of full range. A passage to the vector-valued setting is done. Moreover, an Olsen-type inequality is obtained.
AB - Under the Morrey norm, the fractional integral operator and the fractional maximal operator behave similarly as was initially proved by Adams and Xiao. Later on, Tanaka extended this result. The goal of this note is to extend their results on Morrey–Lorentz norm for exponents of full range. A passage to the vector-valued setting is done. Moreover, an Olsen-type inequality is obtained.
KW - Morrey spaces
KW - Morrey–Lorentz spaces
KW - fractional integral operators
KW - fractional maximal operators
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U2 - 10.1134/S0001434620010071
DO - 10.1134/S0001434620010071
M3 - Article
AN - SCOPUS:85080983037
SN - 1757-7489
VL - 107
SP - 63
EP - 79
JO - Mathematical Notes of the Academy of Sciences of the USSR
JF - Mathematical Notes of the Academy of Sciences of the USSR
IS - 1-2
ER -