Zeitschrift für Analysis und ihre Anwendungen

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Volume 36, Issue 2, 2017, pp. 129–149
DOI: 10.4171/ZAA/1582

Published online: 2017-03-29

Generalized Hardy–Morrey Spaces

Ali Akbulut[1], Vagif Sabir Guliyev[2], Takahiro Noi[3] and Yoshihiro Sawano[4]

(1) Ahi Evran University, Kirsehir, Turkey
(2) Ahi Evran University, Kirsehir, Turkey
(3) Tokyo Metropolitan University, Japan
(4) Tokyo Metropolitan University, Japan

This paper is an off -spring of the contribution [Z. Anal. Anwend. 36 (2017)(1), 17–35]. We propose a way to consider the decomposition method of generalized Hardy–Morrey spaces. Generalized Hardy–Morrey spaces emerged from generalized Morrey spaces. By means of the grand maximal operator and the norm of generalized Morrey spaces, we can defi ne generalized Hardy–Morrey spaces. With what we have culminated for the Hardy–Littlewood maximal operator, we can easily refi ne the existing results. As an application, we consider bilinear estimates, which is the "so-called" Olsen inequality. In particular, our results complement the one in the 2014 paper by Iida, the fourth author and Tanaka [Z. Anal. Anwend. 33 (2014)(2), 149–170]; there were two mistakes. One lies in the decomposition result and another lies in the proof of the Olsen inequality.

Keywords: Generalized Hardy–Morrey spaces, decomposition, maximal operators, Olsen inequality

Akbulut Ali, Guliyev Vagif Sabir, Noi Takahiro, Sawano Yoshihiro: Generalized Hardy–Morrey Spaces. Z. Anal. Anwend. 36 (2017), 129-149. doi: 10.4171/ZAA/1582