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Journal of Function Spaces
Volume 2016, Article ID 3262761, 7 pages
http://dx.doi.org/10.1155/2016/3262761
Research Article

Hadamard Multipliers and Abel Dual of Hardy Spaces

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

Received 18 February 2016; Revised 1 April 2016; Accepted 3 May 2016

Academic Editor: Antonio S. Granero

Copyright © 2016 Paweł Mleczko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper is devoted to the study of Hadamard multipliers of functions from the abstract Hardy classes generated by rearrangement invariant spaces. In particular the relation between the existence of such multiplier and the boundedness of the appropriate convolution operator on spaces of measurable functions is presented. As an application, the description of Hadamard multipliers into is given and the Abel type theorem for mentioned Hardy spaces is proved.