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On the equivalence between weak BMO and the space of derivatives of the Zygmund class

Kwessi Eddy

Demonstratio Mathematica

2021

Vol. 54, nr 1

140--150

In this paper, we will discuss the space of functions of weak bounded mean oscillation. In particular, we will show that this space is the dual space of the special atom space, whose dual space was already known to be the space of derivative of functions (in the sense of distribution) belonging to the Zygmund class of functions. We show, in particular, that this proves that the Hardy space H1 strictly contains the special atom space.

Zygmund inequality of the conjugate function on Morrey-Zygmund spaces

Yee Tat-Leung, Ho Kwok-Pun

Demonstratio Mathematica

2019

Vol. 52, nr 1

97--104

We generalize the Zygmund inequality for the conjugate function to the Morrey type spaces defined on the unit circle T. We obtain this extended Zygmund inequality by introducing the Morrey-Zygmund space on T.