In many branches of mathematical analysis and mathematical physics, the Hardy operator and Hardy inequality are fundamentally important and have been intensively studied ever since the pioneer researches. This volume presents new properties of higher-dimensional Hardy operators obtained by the authors and their collaborators over the last decade. Its prime focus is on higher-dimensional Hardy operators that are based on the spherical average form. The key motivation for this monograph is based on the fact that the Hardy operator is generally smaller than the Hardy–Littlewood maximal operator, which leads to, on the one hand, the operator norm of the Hardy operator itself being smaller than the latter. On the other hand, the former characterizing the weight function class or function spaces is greater than the latter.

�ber die Autorin bzw. den Autor

Shanzhen Lu is a full professor of the Department of Mathematics in Beijing Normal University (BNU). He was President of BNU during the period 1995–1999. Lu's research areas are harmonic analysis and approximation theory. Lu has published more than 200 theses (including co-authored ones) in both Chinese and international mathematics periodicals. He has also published 7 books (including co-authored ones), 5 of which are written in English. Lu was awarded the Outstanding Achievement Award of the State Education Commission (1985), the First Prize for Progress in Science and Technology of The State Education Commission (1988), the Fourth Prize of the National Prize for Natural Science (1989), the Second Prize of the National Prize for Natural Science nominated by the Ministry of Education (2003), the Young and Middle-Aged Expert Nationally Acknowledged for their Outstanding Achievements (1990), and the National Outstanding Science and Technology Worker of Higher Education (1990).

Zunwei Fu is a full professor and currently works at the School of Mathematics and Statistics, Linyi University. He does research in harmonic analysis and was sponsored by the National Natural Science Foundation of China (Grant No. 12071195).

Fayou Zhao is a full professor and currently works at the Department of Mathematics, Shanghai University. He does research in harmonics analysis and was sponsored by the National Natural Science Foundation of China (Grant No. 11971295) and Natural Science Foundation of Shanghai (Grant No. 19ZR1417600).

Shaoguang Shi is a full professor and currently works at the School of Mathematics and Statistics, Linyi University. He does research in harmonic analysis and was sponsored by the National Natural Science Foundation of China (Grant No. 11771195) and Natural Science Foundation of Shandong Province (Grant Nos. ZR2019YQ04, 2020KJI002).

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