Main Article Content
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.
- 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.
- H ¨ormander. L., The Analysis of Linear Partial Differential Operators II, Springer-Verlag, Berlin Heidelberg New York, 1983.
- John. F. and Nirenberg. L., On functions of bounded mean oscillation , Communications on Pure and Applied Mathematics, 14 (1961), 415-426.
- 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.
- Singh. S. K., The S-transform on spaces of type S, Integral Transforms and Special Functions, 23(7) (2012), 481-494.
- Singh. S. K., The S-transform on spaces of type W, Integral Transforms and Special Functions, 23(12) (2012), 891-899.
- Singh. S. K., The fractional S-transform of tempered ultradistibutions, Investigations in Mathematical Sciences, 2(2) (2012), 315-325.
- Singh. S. K., The fractional S-transform on spaces of type S, Journal of Mathematics, 2013 (2013), Article ID 105848.
- Singh. S. K., The fractional S-transform on spaces of type W, Journal of Pseudo-Differential Operators and Applications, 4(2) (2013), 251-265.
- Singh. S. K., A new integral transform: Theory part, Investigations in Mathematical Sciences, 3(1) (2013), 135-139.
- Singh. S. K., The S-Transform of distributions, The scientific world journal, 2014 (2014), Article ID 623294.
- 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.
- 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.