Abstract
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.
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Acknowledgements
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.
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Hatano, N. Fractional Operators on Morrey—Lorentz Spaces and the Olsen Inequality. Math Notes 107, 63–79 (2020). https://doi.org/10.1134/S0001434620010071
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DOI: https://doi.org/10.1134/S0001434620010071