Research Article
The S-Transform on Hardy Spaces and Its Duals
- Rajiv Gandhi University, Arunachal Pradesh, INDIA
* Corresponding author
Abstract
In this paper, continuity and boundedness results for the continuous S-transform in BMO and Hardy spaces are obtained. Furthermore, the continuous S-transform is also studied on the weighted BMO$_k$ and weighted Hardy spaces associated with a tempered weight function which was proposed by L. H\"ormander in the study of the theory of partial differential equations.
How to Cite
S. K. Singh, B. Kalita, The S-Transform on Hardy Spaces and Its Duals, Int. J. Anal. Appl. 7 (2015), 171–178.
BibTeX
@article{Singh2015,
author = {Singh, Sunil Kumar and Kalita, Baby},
title = {The S-Transform on Hardy Spaces and Its Duals},
journal = {Int. J. Anal. Appl.},
volume = {7},
year = {2015},
pages = {171--178},
doi = {}
}References
- [1] Chuong. N. M. and Duong. D. V., Boundedness of the wavelet integral operator on weighted function spaces, Russian Journal of Mathematical Physics, 20(3) (2013), 268-275.
- [2] H ¨ormander. L., The Analysis of Linear Partial Differential Operators II, Springer-Verlag, Berlin Heidelberg New York, 1983.
- [3] John. F. and Nirenberg. L., On functions of bounded mean oscillation , Communications on Pure and Applied Mathematics, 14 (1961), 415-426.
- [4] Pathak. R. S. and Singh. S. K., Boundedness of the wavelet transform in certain function spaces, Journal of inequalities in pure and applied mathematics, 8(1) (2007), Article 23, 8 pages.
- [5] Singh. S. K., The S-transform on spaces of type S, Integral Transforms and Special Functions, 23(7) (2012), 481-494.
- [6] Singh. S. K., The S-transform on spaces of type W, Integral Transforms and Special Functions, 23(12) (2012), 891-899.
- [7] Singh. S. K., The fractional S-transform of tempered ultradistibutions, Investigations in Mathematical Sciences, 2(2) (2012), 315-325.
- [8] Singh. S. K., The fractional S-transform on spaces of type S, Journal of Mathematics, 2013 (2013), Article ID 105848.
- [9] Singh. S. K., The fractional S-transform on spaces of type W, Journal of Pseudo-Differential Operators and Applications, 4(2) (2013), 251-265.
- [10] Singh. S. K., A new integral transform: Theory part, Investigations in Mathematical Sciences, 3(1) (2013), 135-139.
- [11] Singh. S. K., The S-Transform of distributions, The scientific world journal, 2014 (2014), Article ID 623294.
- [12] Stockwell. R. G., Mansinha. L. and Lowe. R. P., Localization of the complex spectrum: The S transform, IEEE Trans. Signal Process., 44(4) (1996), 998-1001.
- [13] Ventosa. S., Simon. C., Schimmel. M. , DaËœnobeitia. J. and M`anuel. A., The S-transform from a wavelet point of view, IEEE Trans. Signal Process., 56(07) (2008), 2771-2780.